In his letter to Hiranya, the President of the APS, Homer Neal, states:
“It is my pleasure to inform you that you have been elected Fellow of the American Physical Society (APS) by the APS Council of Representatives at its September 2016 meeting upon the recommendation of the Division of Astrophysics. The number of APS Fellows elected each year is limited to no more than one half of one percent of the membership. It is a prestigious recognition by your peers of your outstanding contributions to physics …. For significant contributions to the Wilkinson Microwave Anisotropy Probe project, Planck analyses, and the application of advanced statistical techniques to a wide range of astronomical data.”
Read all about it in the UCL Press Release!
Congratulations to Hiranya Peiris on her recent appointment to Director of the Oskar Klein Centre for Cosmoparticle Physics in Stockholm! Her new position means that Hiranya will be sharing her time (~50/50) between the Oskar Klein Centre and UCL for up to 5 years. Read Ariel Goobar’s welcoming post as the outgoing director.
With the end of session, we also say a fond farewell to several members of the team as they move on to pastures new; including Franz Elsner, Nina Roth, Michelle Lochner and Marc Manera, and also to Will Handley who joined us for a gap postdoc before embarking on a Junior Research Fellowship at Caius College, Cambridge.
Hiranya Peiris gave a lecture at the Royal Institution recently, on how over the past decade we have been able to answer age-old questions accurately, such as how old the Universe is, what it contains, and its destiny.
Join her as she unravels the detective story, explaining what we have uncovered, and how we know what we know!
This post was written by Daniela Saadeh.
This work has been published in Physical Review Letters today, and we are thrilled to note that the paper has been selected for Editors’ Suggestion! It has also featured in APS Physics and Science magazine, and in a UCL press release today!
The Standard Model of Cosmology relies on the fundamental assumption that we don’t occupy a special place in the Universe, an idea known as the Copernican Principle. After centuries of assuming humans were obviously at centre of the Universe, we got tired of being so egocentric!
‘Not in a special place’ is an idea that converts into the assumptions that the large-scale Universe looks the same everywhere, and as seen from everywhere; in particular, its properties don’t depend on position (a concept known as homogeneity) or direction (isotropy). However, assumptions must be tested. We can’t observe the Universe from other places (we are still sadly bound to the Earth and surroundings) but we can see what it looks like in different directions. Then we can decide how likely it is that the Universe is isotropic or not.
So we did just that and we had a go at putting the assumption of isotropy to the test. To do so, we analysed the Cosmic Microwave Background (CMB), a left-over radiation from the Big Bang that is basically a snapshot of the Universe when it was just 400,000 years old (compared to about 14 billion years now – a baby Universe indeed!). Looking this far allows us to probe very large scales, which is precisely what we needed to do.
Fortunately, we have amazing data from the Planck satellite with a wealth of quantitative information about the CMB temperature and polarization – what’s not to love?!
The isotropic picture
In a perfectly homogeneous and isotropic Universe the CMB would look likewise perfectly homogeneous and isotropic. However, during the very early phases of the Universe history (particularly, during a period known as inflation), this otherwise slightly boring picture was spiced up a bit and small perturbations were created in this smooth landscape in the form of curvature fluctuations. These incidentally, went on to form all the structure we know today – galaxies, clusters of galaxies, etc., and are the reason why we can exist today and discuss anisotropy! These perturbations can be studied by analysing the tiny temperature and polarization differences that were imprinted in the CMB as a result, which are represented as coloured blots in the CMB map in Figure 1. They are really tiny perturbations: 1 part in 100,000. As far as we can see, large-scale isotropy is at least, a very good approximation. As far as homogeneity is concerned, we can only comment on the portion of the Universe we see, but here large-scale homogeneity certainly seems to also hold.
In the standard picture, only these tiny fluctuations generated during inflation leave their imprint on the CMB. A distinctive feature is that some randomness is involved in their generation; their statistical behaviour is constrained by physics, but what exact perturbation will appear at a precise spot is random. If we were to make an analogy with a coin toss, we could say that physics chooses the coin, but the particular outcome of a toss is then random.
The anisotropic picture
What happens if isotropy is broken?
We considered the case where homogeneity is still preserved i.e. the properties of the Universe depend on direction, but in the same way in every place in the Universe. This is known as a Bianchi cosmology after the 19th century mathematician Luigi Bianchi (his precious 1898 paper is so old that is not even available in modern Italian!).
Let’s first see how the Universe can be homogeneous but anisotropic with a simple (very simple!) example. The animation below shows a fictitious homogeneous but anisotropic universe expanding at different rates in different directions, but the same way at every point. The triangle, square and circle are all deformed as a result but in the same way (in principle, the triangle could experience a different stretch from the circle). Let me stress this is only the simplest example; anisotropy can actually take much more complicated forms!
In such a Universe, the light making up the CMB is also stretched i.e. redshifted differently depending on the direction it is travelling. This means we could for example, see the light coming from north and 30º above the horizon as being redder (larger wavelength, more stretched) and that coming from west and 60º above the horizon as being bluer (lower wavelength, less stretched). In other words, this differential expansion will leave an imprint on the CMB.
So, in Bianchi cosmologies we will have two different types of CMB imprints: those generated during inflation discussed above, and the ones created by this intrinsic direction-dependence of the Universe. The big difference between them is that the latter can be predicted exactly, that is, it’s completely deterministic. For example, in a Universe expanding as in the animation above, the CMB would look as shown in Figure 2 below.
This was just a simple example. Moving away from the simplest picture, there are several ways in which the Universe can be anisotropic. In this website, you can see animations displaying how the CMB varies for some of these ways – for its visual aesthetics, I recommend this one!
Looking for anisotropy
So, now we have discussed what anisotropy is, let’s discuss how we can go and search for it.
In his blog post, Jason McEwen discussed how Early Universe @UCL people had developed a rigorous Bayesian statistical analysis tool (called ANICOSMO) to search for signatures of anisotropic universes.
Briefly, ANICOSMO works as follows. First it needs a prediction of what the CMB will look like in a certain anisotropic universe (panel 1 in Figure 4). To do this, we have developed our own code called ABSolve, which can predict the pattern that Bianchi universes imprint on the CMB temperature and polarization. Then it needs to know the statistical properties of the perturbations generated during inflation (panel 2): for this we use the publicly available CAMB. ANICOSMO then puts these two bits of information together and obtains a prediction for the complete CMB sky after both anisotropy and inflation have done their job (panel 3). This simulated CMB is then compared with the real one and ANICOSMO can determine how much similar they look. This procedure is repeated for all the universes that are viable based on what we already know.
To carry out this study, we further expanded ANICOSMO (which is now known as ANICOSMO2) to analyse CMB polarization data as well as temperature. This signal is in fact, super precious because it has the most constraining information for anisotropy.
So is the Universe anisotropic?
No! The simpler picture wins! Our study disfavours anisotropic expansion of the Universe with odds of 121,000:1 against! (No bookmaker will give you that!)
After searching for all the possible ways that the Universe can be anisotropic, we concluded that there is not evidence for any of them. The Universe just appears to like all its directions the same!
Many thanks to Bruno Moraes for his helpful comments.
You can read more here:
D. Saadeh, S. M. Feeney, A. Pontzen, H. V. Peiris, J. D. McEwen
How isotropic is the Universe?
D. Saadeh, S. M. Feeney, A. Pontzen, H. V. Peiris, J. D. McEwen
A framework for testing isotropy with the cosmic microwave background
A. Pontzen, A. Challinor
Linearization of homogeneous, nearly-isotropic cosmological models
A. Pontzen, A. Challinor
Bianchi Model CMB Polarization and its Implications for CMB Anomalies
“I will aim to be a strong advocate for an inclusive Society that represents and supports the interests of the full range of demographics of its membership, and especially that of junior researchers.”
“I am thrilled to have been awarded a NASA Einstein fellowship, which will allow me to stay at New York University for three more years and realise an ambitious research programme in optimal conditions. I plan to take advantage of the stability and freedom offered by this fellowship to search for imprints of primordial physics in the large scale structure of the universe and also develop statistically accurate ways to test detailed models of galaxies and quasars using the large data sets that are or will be available in the next decade. In particular, I’d like to draw more connections between the various types of experiments, such as imaging surveys (DES, LSST), spectroscopic surveys (eBOSS, DESI) and others (SphereX, WFIRST). Given UCL’s involvement in these projects and the expertise of the Early Universe group, I will continue to visit London on a regular basis and be part of exciting collaborative projects.”
The LSST is an international project that UCL astronomers including our very own Hiranya Peiris have been involved in since 2013.
Read all about it on the UCL Mathematical & Physical Sciences News page!
We are delighted to be able to report that in the Royal Astronomical Society announcement of the 2016 winners of its awards, medals and prizes, the Society’s 2016 Fowler Award for early achievement in astronomy has been made to our very own Andrew Pontzen!
Here is the Royal Astronomical Society citation of the award:
The Fowler Award for Astronomy is awarded to Dr Andrew Pontzen.
Andrew Pontzen is an exceptionally creative theorist. He has done important work in a number of different areas spanning the range from theoretical work on anisotropic cosmologies, numerical simulations of galaxy formation, through to the dynamics of dark matter halos. His work on the effects of supernovae feedback in flattening the inner density profiles of dwarf galaxies offers a solution to a long-standing problem of the Cold Dark Matter model. In recognition of his unusual combination of analytic ability, computational skills and originality, Andrew Pontzen receives the Fowler Award of the Royal Astronomical Society.
Congratulations to Andrew on this phenomenal success!
This blog post was written by Andrew Pontzen.
Come trick-or-treating at my house and you’ll be treated to little more than an icy stare. In my book, the only good thing about Halloween is its ability to hold back the tidal wave of commercial Christmas tat that floods shops in November. Let’s face it, the most famous ghost of Hallowe’en is the mysterious apostrophe that died under suspicious circumstances in the 1990s, yet is still occasionally sighted floating through the word.
Most years, Early Universe @ UCL gang members can be found out on the streets of London, terrorising law-abiding citizens into giving up sweets, cakes and bubble universes. But with the departure of notorious enforcer Leistedt to the meaner streets of New York, this time the leadership has taken a softer stance and members have instead been carving out new niches in the traditional pumpkin competition.
Runner-up is Hiranya’s Einstein homage, which I like to think was carved using “spooky action at a distance”:
But the winner is newcomer Luisa Lucie-Smith with a Churchillian masterpiece:
A last-minute appeal to the judges objected that carrots are contraband. The appeal has been denied.
This post was written by Michelle Lochner.
A few months ago, Google made headlines when they released images of “dreams” from their image recognition neural network. In a process they called “Deep Dreaming”, the neural network could turn any normal image into a fantastical dreamscape, all generated from things the network has seen while training. I decided to experiment with Google’s publicly available deep dreaming tools and asked the question, what does the CMB look like when the network dreams about it? This post below is reproduced from my research blog, http://doc-loc.blogspot.co.uk/.
You may have heard about Google’s Deep Dreaming network, turning completely normal pictures of clouds into surreal cityscapes.
I was curious about what would happen if I asked the network to dream about the cosmic microwave background (CMB), the baby photo of the Universe. The CMB is the background radiation left over by the Big Bang and is one of the most important probes of the Universe that we have. As a pattern, it looks pretty close to noise so I had no way of knowing what might come out of Google’s dreams.
What is Deep Dreaming? Well this all came from the desire for search-engine giant Google to solve the image-recognition problem. This is a good example of something that humans do very easily at just a few weeks of age, but is notoriously difficult to get a computer to do. However, Google does seem to be cracking the problem with their deep learning algorithms. They’re using convolutional neural networks, which are neural networks with many layers. So it seems Google has had the most success with a machine learning algorithm that tries to imitate the human brain.
Deep Dreaming is what I suspect the people at Google came up with while they were trying to understand exactly what was going on inside their algorithms (machine learning can be a dark art). The original blog post is excellent so I won’t repeat it here but will rather show you what I got when playing around with their code.
You can actually submit any image you like here and get a ‘inceptionised’ image out with default settings, but I wasn’t happy with the result (the default settings seem optimised to pick up eyes) so I decided to dig deeper. For the technically inclined, it’s not that hard to run your own network and change the settings to get the strange images in Google’s gallery. Everything you need is on the publicly available github repository, including a great ipython notebook for doing this yourself.
I took a (relatively low-resolution) image of the CMB from the Planck satellite to test the deep dreaming methods on. Basically all of the DeepDream images are produced by picking something and then telling the neural net to try and make the input image as close to that thing as possible. It’s the something you pick that will change the images you get out.
Google’s trained convolutional neural network is over a hundred layers deep, each layer corresponding to some particular things the network has seen in the training set. When running the network on an image, you can pick out one of the layers and enhance it.
Picking out higher level layers tends to bring out smaller, more angular features whereas lower levels tend to be more impressionistic, smoother features.
Then you can also ask the network to try and find something particular within your image. To the technically inclined, this is equivalent to placing a strong prior on the network so that it optimises for a particular image. In this case, I asked it to find flowers in the CMB.
Now comes the fun stuff. You ask the network to generate an image as before, focusing on a specific layer. Then you take the output image, perform some small transform (like zooming in a little) and run it again. This is Google’s dreaming. You can start with almost any image you like. Playing around I eventually found “the dog layer” where it continuously found dogs in the sky.
I made a video of a few hundred iterations of this (note: I lengthened the first few frames otherwise they go by way too fast). I find it really appropriate that after a while, it starts finding what really looks like a bunch of microwaves, in the cosmic microwave background radiation… Enjoy the show!
As usual at this time of year we have to bid farewell to some familiar faces in the Early Universe @ UCL team, and also welcome some new faces!
We bid a fond farewell to Boris Leistedt as he takes up a new position as a Simons Fellow at New York University. It isn’t goodbye however as Boris will return regularly as a long term visitor to the group, and will continue to contribute to this blog!
We also say goodbye and good luck to Aurélien Benoit-Lévy as he takes up a CNES postdoctoral fellowship at Institut d’Astrophysique de Paris.
Last but not least, we welcome our new PhD student Luisa Lucie-Smith. Luisa did her MSc in Quantum Fields and Fundamental Forces which focussed on theoretical high-energy physics, and her BSc in mathematical physics. She therefore has a strong mathematical/theoretical physics background, and we look forward to her upcoming blog posts!
The summer has brought some well-deserved recognition for EarlyUniverse.org researchers!
Nina Roth received the best poster prize at a major summer symposium held at the European Southern Observatory headquarters in Garching, Germany, titled “Theoretical and Observational Progress on Large-scale Structure of the Universe”.
“I really enjoyed the conference and my collaborators and I are honored by the recognition for our project. The selection committee certainly had a tough decision to make when choosing between ~60 excellent posters. I was especially delighted to receive an ESO shirt as part of the prize, because I collect university-themed clothing!”
Daniela Saadeh has received the 2015 Physics of the Dark Universe Award at the conference “From Inflation to Galaxies: a workshop in honor of Sabino Matarrese”, which came accompanied by a fun giant cheque!
“The conference was a very friendly place for a young person to speak and I could give free rein to my enthusiasm and excitement. There were very good talks, so I feel honoured and extremely happy about this award, especially because it comes after a lot of hard work!”
Meanwhile Boris Leistedt, whose thesis previously won a prize from the Royal Astronomical Society, has been given a nice parting present from UCL as he begins his new position as a Simons Fellow at New York University. He has been jointly awarded the Jon Darius Memorial Prize for 2014/15, for Outstanding Postgraduate Research in Astrophysics.
Boris Leistedt’s PhD thesis (“Accurate Cosmology with Galaxy and Quasar Surveys”) has been named runner-up for the Michael Penston Prize 2014, awarded for the best doctoral thesis in astronomy and astrophysics. Boris says:
“I am honoured to be the runner-up for the Michael Pentson Prize 2014. It took me by surprise given how competitive this prize is, but I am delighted to see that my thesis convinced the selection committee at the Royal Astronomical Society. I am also pleased to perpetuate a UCL tradition started by Stephen Feeney and Emma Chapman, who both did their PhD in the UCL cosmology group and were named runner-ups for the same prize in 2012 and 2013. Go UCL!”
Boris will be taking up a Junior Fellowship of the Simons Society at New York University in September 2015. We wish him all the best!
The European Research Council project CosmicDawn has passed its mid-term milestone, and the mid-term report has just been approved by the ERC! Led by Hiranya Peiris, the CosmicDawn team funded by the ERC during this reporting period consisted of postdoctoral research fellows Jonathan Braden, Franz Elsner, Boris Leistedt, and Nina Roth, as well as undergraduate intern Max Kerr Winter.
The CosmicDawn team is using the Planck and Dark Energy Survey (DES) data to rigorously test the theory of inflation, the dominant paradigm for the origin of cosmic structure, and to seek signatures of new physics that are likely to exist at these unexplored energies. Our aim is to go beyond simply testing generic predictions of the inflationary paradigm, to gain a fundamental understanding of the physics responsible for the origin of cosmic structure. In working towards this goal, the team has focused on: (1) theoretical modelling at the cutting edge of fundamental physics (describing not just the inflationary period but also pre- and post-inflationary physics); (2) development of powerful wavelet and filtering techniques to extract these physical signatures; (3) introduction of CMB techniques new to LSS analyses to facilitate major sensitivity gains; (4) use of advanced Bayesian statistical methods to extract reliable information from the data; and (5) a deep understanding of data limitations and control of systematics. Over the reporting period, our research has led to 74 publications, including interdisciplinary papers with high energy theorists and numerical relativists, and cross-disciplinary papers in information engineering and high performance computing.
This post was written by Jonathan Braden.
NOVA’s The Nature of Reality recently dedicated a blog post to my work on bubble collisions with J. Richard Bond and Laura Mersini-Houghton. The post focussed on one possible observational consequence of our findings. Here I’ll outline a little more precisely what we did in our work. For more information see my webpage.
Inflation, Bubble Universes and the Multiverse
Modern cosmology posits that the very early universe underwent a period of rapid expansion known as inflation. Inflation smoothes out the cosmos, creating the large-scale homogeneity we observe today, while simultaneously leaving small wrinkles that eventually form structures such as galaxies. However, it turns out that once inflation begins it may continue forever. In this ‘eternal inflation’, an omniscient being able to view the entirety of the universe at once would see vast swathes of space continuing to inflate. Only in special pockets has inflation ended, allowing structures such as galaxies to form and life as we know it to exist. This large collection of “pocket universes” is one incarnation of the multiverse.
Two mechanisms may cause eternal inflation, both of which can be visualized by thinking about a ball rolling down a mountain. The multiverse can be pictured as many copies of this mountain, each located at a different point in space and each with its own ball. New space is created in regions that are inflating, so the mountains in these regions replicate to fill the rapidly expanding space. The rate at which space is being created, or how quickly a given mountain replicates, is determined by the height of the ball above sea level. When a ball approaches the bottom of a mountain, inflation ends in that region. The mountains aren’t completely smooth: there are many ridges, long valleys and depressions along the way, which affect the ball’s trajectory and determine how long it takes to reach the base. There are also regular wind gusts that get stronger as we climb higher up the mountain. The mountaintop is extremely windy, while the base is calm. The wind represents the effects of quantum mechanics on the rolling balls and is produced by inflation. The strength and direction of the gusts varies from mountain to mountain. However, each individual gust affects a large spatial volume and thus pushes the balls on several different mountains at the same time.
In one type of eternal inflation, which I’ll call stochastic eternal inflation, the wind is so strong that it can push the ball back up the mountain. Balls that move up the mountain then replicate, so that there are always some balls that remain trapped near the top of the mountain, i.e. some regions of space are always inflating.
In the second type of eternal inflation, called false vacuum eternal inflation, the ball instead rolls into a depression and gets stuck. Without quantum mechanics, this would be the end of the story and the ball would sit there forever. However, the ball may escape in two different ways. In one case, the wind is strong enough to blow the ball out of the depression and it once again starts rolling down the hill. In the other case, the depression is so deep that the wind can’t extract the ball from it. However, there is another quantum mechanical effect. As an (imperfect) analogy, suppose that thunderstorms occasionally pass over the mountain and the rain fills the depression so that it forms a pond. Eventually the pond overflows and the ball escapes with the water to once again start rolling down the mountain. In physics lingo, the region has quantum mechanically tunnelled out of the depression. The thunderstorms are more localised than the wind gusts, so the regions that tunnel are smaller than the regions blown around by the wind. In the actual universe these tunnelling events correspond to the creation of new bubble universes.
In this final scenario, the universe on very large scales looks like a pot of boiling water, with a universe like our own existing within each of the bubbles of steam. The water in this case has the strange property that it is continually expanding and replenishing itself, so that the pot of water gets larger and larger. As a result, new water is constantly becoming available to nucleate new bubbles. Once in a while two bubbles will nucleate close enough to each other that they run into each other as they expand. From our viewpoint living within one of the steam bubbles, it looks as though our universe has collided with another universe.
Previously, physicists have always assumed that if we were to videotape a collision between two bubbles, then the video would look exactly the same if we spun the video camera around in certain ways or if we jumped in a car and drove away from the two bubbles at a constant speed in certain directions. To use a physicist’s favourite word, the collision is said to possess a large amount of symmetry. The symmetry is really a combination of two different types of symmetries: a rotational piece and two boost pieces. These correspond to rotating our video camera and driving away in a car, respectively. To visualize the rotational part, first imagine that each bubble is a perfectly spherical ball. In a collision we have two balls, so imagine connecting the two bubbles by a thin string to make a barbell. After nucleating, each bubble expands so the length of the string decreases with time until eventually the bubbles collide. Now, if you grab one ball in each hand and rotate the whole thing around this string, the collision will look exactly the same. The boost symmetry is a little bit stranger, but basically if you took one ball in each hand and threw them away from you at the same speed and with their centres parallel to each other, then the resulting collision will be the same regardless of how fast you throw the two balls.
When we make these symmetry assumptions, then we often get collisions that look like the figure below. To visualize what’s going on, think of each bubble as a rubber ball that is being inflated while its center is held fixed. As they are inflated, each ball gets bigger and bigger, just like a balloon. Eventually the balls become large enough that they hit each other. When the rubber walls of the balls collide, they bounce off of each other, making a dent. These dents then spring back out and bounce off each other again, and the whole process repeats. A video illustrating this can be seen in the YouTube link below.
Collisions with Quantum Mechanics
However, the situation described above isn’t the full story. Thanks to quantum mechanics, there is inevitably some jitter around the perfect spheres. To use the same analogy I gave in the article, imagine that each bubble is a globe with small bumps and ripples from the various land masses, mountains, and valleys. If we spin the globe around, the positions of the continents, oceans, and mountain ranges change so that it no longer looks identical when viewed from different directions. Once again using a physicist’s language, we say the symmetry has been broken.
As I mentioned, these mountain ranges and valleys must be present, or else we would be violating the laws of quantum mechanics. However, they also serve two much more practical purposes in the inflationary multiverse: the bubbles nucleate because of the quantum jitter, and the quantum fluctuations eventually form all of the galaxies and other structure that we see in the universe around us. Therefore, the entire picture of our observable universe living within a bubble nucleated in a much larger multiverse relies heavily on this quantum jitter.
In our series of papers (here, here and here) we studied the effects of this quantum jitter on bubble collisions. When the bubbles first nucleate, the fluctuations are small and you would have to look very carefully to see that the bubbles are not perfect spheres. Again viewing each bubble as a globe, you would need to pull out a magnifying glass in order to see that there are small mountains on the surface. However, it turns out that the collisions of the bubbles can make the jitter grow very fast. In the figure below, I’ve illustrated the difference between having no quantum jitter (left panel) and small initial fluctuations (right panel). The collision with the initial jitter is seen in the YouTube video below. The mountains (valleys) on the parts of the globes that dent in and out during the collision quickly grow in height (depth). In other words, mountain ranges grow on the parts of the walls that continually bounce off of each other. The first few times the bubble walls bounce off of each other, the mountains are still small so things look basically the same as if the bubbles were perfect spheres. However, it doesn’t take long for the mountains to get very high (much higher than Mount Everest). In the next collision, rather than the walls of the balls bouncing off of each other, the mountains instead poke holes in the bouncing walls. The walls quickly dissolve, leaving behind some small remnants in the collision region.
New Phenomenology and Future Work
As seen in the figures and videos above, including quantum fluctuations can significantly alter the outcome of bubble collisions. This forces us to re-evaluate our current understanding of bubble collisions in the multiverse. Two of the more exciting possibilities are the production of gravitational waves during the pairwise collisions of bubbles, and the creation of black holes from the collisions. In the treatment based on rotational and boost symmetries, both of these effects are ignored because the symmetry assumptions forbid them from occurring. The former of these effects was emphasized in the NOVA post on our work, and it could provide a new observational signature from bubble collisions in the multiverse. This is very exciting, since this could give us an additional observational handle with which to test the multiverse.
A big thank-you to Belle Helen Burgess and Hiranya Peiris for editing and comments.
You can read more here:
NOVA blog post
Gravitational Waves from Bubble Universe Collisions?
More on bubble universe collisions
- Eternal Inflation and Colliding Universes
- The World Inside a Bubble
- Simulating Cosmic Bubble Collisions in Full General Relativity
J.R. Bond, J. Braden, and L. Mersini-Houghton
Cosmic bubble and domain wall instabilities III: The role of oscillons in three-dimensional bubble collisions
J. Braden, J.R. Bond, and L. Mersini-Houghton
Cosmic bubble and domain wall instabilities II: Fracturing of colliding walls
J. Braden, J.R. Bond, and L. Mersini-Houghton
Cosmic bubble and domain wall instabilities I: Parametric amplification of linear fluctuations
Photograph by Boris Leistedt
In honour of International Women’s Day, in this blog post UCL women who work on the Dark Energy Survey (DES) talk about what most excites them about their research on DES!
The Dark Energy Survey is designed to probe the origin of the accelerating universe and help uncover the nature of dark energy by measuring the 14-billion-year history of cosmic expansion with high precision. More than 120 scientists from 23 institutions in the United States, Spain, the United Kingdom, Brazil, and Germany are working on the project. This collaboration has built and deployed an extremely sensitive 570-Megapixel digital camera, DECam. This new camera has been mounted on the Blanco 4-meter telescope at Cerro Tololo Inter-American Observatory, high in the Chilean Andes.
Starting in August of 2013 and continuing for five years, DES has begun to survey a large swathe of the southern sky out to vast distances in order to provide new clues to this most fundamental of questions.
UCL hosts a large group of researchers contributing heavily to DES, and the optical corrector for the survey camera was built here. You can read more about DES @UCL here.
DES@UCL women in their own words:
Antonella Palmese (PhD student): “DES is not only about Dark Energy. DES is much more: what strikes me the most is the fact that we can discover so many different things with it. When I joined the collaboration one year ago, I would have never expected to work on such a wide range of topics: from the distribution of mass in clusters of galaxies, to the redshifts of the galaxies, to the stars.”
Dr Stéphanie Jouvel (postdoctoral research fellow): “I’m working on photometric redshift systematics: how to get a reliable estimate of the radial distance between our galaxy and galaxies we observe in DES. Spectroscopy being time-intensive and expensive, we have to rely on some photometric bands to get a rough idea of the distance. The distance will then be incorporated in the weak-lensing mass maps or large scale clustering to understand the evolution of structures in the Universe as we go back in time.”
Dr Hiranya Peiris (faculty): “While DES was designed to uncover the secrets of Dark Energy, it is also a huge galaxy survey, mapping an unprecedented volume of the Universe with exquisite precision, so the range of DES science is immense. I am working on using DES data to test fundamental physics, but also to understand astrophysics: how do galaxies form and evolve, and how are they connected to the underlying “scaffolding” of dark matter? I am most excited about answering these questions by combining DES data with other big datasets, such as the cosmic microwave background.”
Lucinda Clerkin (PhD student): “I’m looking at the relationship between dark matter and the stuff that we can see, using galaxies observed by DES along with reconstructed mass maps from weak gravitational lensing. This relationship is an important ingredient in calculations of the make-up and evolution of the Universe, and therefore in figuring out what dark energy is – or indeed if it exists! I’ve also been lucky enough to spend an awesome week observing for DES at the Blanco telescope in Chile.”
We are very pleased to announce that there is a new Doctor in the house! Boris Leistedt passed his PhD viva titled “Accurate Cosmology with Galaxy and Quasar Surveys” with flying colours. We also celebrate Boris’s success in the recent postdoctoral job season: having received offers of several prestigious fellowships in the USA and Europe, Boris has decided to take up a Simons Fellowship at New York University to continue his highly innovative work in survey cosmology. Congratulations and best wishes to Dr. Leistedt!
This guest blog post was written by Layne Price.
I’ll let you in on a little secret about inflation: we don’t know really know any of the details. This might or might not be surprising to you, but it’s not often advertised — although it does keep us working hard!
Let’s start with what we do have: a nice and simple understanding of a basic inflationary mechanism, which has lots of successes — namely, flattening, smoothing, but ever-so-slightly wrinkling our universe. These are things that we do observe and that most people agree we don’t have a satisfactory description for, outside of invoking inflation.
So, what’s the problem?
This simple understanding falls well short of what is actually going on. Inflation happens during a complex era of the universe’s history, which has energies that vastly exceed anything we will likely ever be able to test in a laboratory. Importantly, we do not have an experimentally confirmed theory that we can study for clues at this energy scale, since physics’ workhorse, the Standard Model, breaks down spectacularly.
Consequently, the inflationary models we use are by-and-large “toy” descriptions of something realistic, but beyond our current reach. What I mean by this is that we try to pare down a complicated theory by ignoring possible features it might contain until we are left with only the bare essence of what we need in order to get inflation. We then study this overly simplistic toy model because it’s easier and captures the most important details.
Unfortunately, while this is simple (and Ockham would certainly approve), these toy models have been found lacking. The most obvious problem is that the simplest of all possible models — inflation driven by one single massive field — is under very serious pressure from the Planck satellite, since it predicts more gravitational waves than we can reconcile with the observations of the cosmic microwave background (CMB).
So, if the simplest models don’t work, what are we supposed to do? Let’s say we want to cook up a better inflation model. To start with, we first want to find some sort of exotic material to drive inflation, but there’s nothing obvious in the standard theories. OK, then — what non-standard ingredients do we have? A typical roll-call from high energy theories goes something like this: supergravity; Type I, Type IIa, Type IIb, and heterotic string theories; modified gravity; compactifications of extra dimensions into a high-dimensional landscape; a buffet of supersymmetric extensions to the Standard Model; axions, instantons, galileons — and this just scratches the surface. It’s confusing and unlikely that we will all come to an agreement about exactly which ingredients are right.
However, what each of these theories gives us is the freedom to add lots of new knobs and dials we can play with to tease out a combination of parameters that gives us something sensible. With a complicated enough machine hooked up to the toy models, it’s not so surprising that we can tune it to find lots of interesting things that match the data very well.
So, now we ask ourselves, “Do we find this approach convincing?” If we were to include everything in the fridge in our recipe, weigh all our ingredients precisely, cook the theory just right, and get a great new scenario, would you believe it? We may be very fond of the exact combination of knobs and dials we tuned to predict the data, but of course there is nothing to guarantee that this is what actually happened in the real Universe – many different settings could have led to the same outcome!
Luckily there’s something we can do so that we don’t have to have a complete understanding of the high energy theory. Suppose we have an inflation model with one parameter X, and we need X to get a prediction, which we’ll call Y, from the model. Inflationary parameters might be things like a quantum field’s mass or initial conditions; and, as we discussed above, realistic models have many parameters. But, we’ll use X as a placeholder in a general model.
It’s common that we don’t know what the exact value of X is. High energy theory is notoriously hard, after all. So, it’s typical to quit and leave the problem here, since we’re now stuck: we don’t know X, and Y depends on X, so we need more info. However, we do have some extra information floating around somewhere; we just need to gather it.
Let’s collect what we do know in this hypothetical example:
- Well, I suppose X should be positive and that X=10,000 is unrealistically high, for whatever reason.
- However, X=1, X=10, X=100, and X=1,000 all seem like they are perfectly reasonable values.
- If X=1, then I can calculate Y=1; if X=10, then Y=2; if X=100, Y=3; etc.
We will use this information by first drawing an analogy between “uncertainty in X” and “a random variable X.” Because we are uncertain about the exact value of parameter X, we can instead randomly set the dial that tunes this parameter according to our beliefs outlined above. We calculate the prediction Y and think of this as one of many possible values Y could have. We then repeat the process many times to build a large sample of the model’s prediction. Instead of having one simple prediction, the model then has a range of possible predictions that are weighted according to this random sample. The hope is that a good model will have a small spread for its predictions.
In our recent paper we took this a step further and used the power of the Central Limit Theorem to give us easily characterized results for the CMB, in terms of far fewer parameters than you might naively expect. The Central Limit Theorem says that independent random variables (our model’s parameters) act like a single normally distributed variable when you add a bunch of them together. A normal distribution has only two parameters, the mean and variance, which effectively cancels out a lot of the model’s complexity, leaving only a few dials that we can tune in our inflationary machinery.
We did this for one of the most interesting observables, which is called the “inflationary consistency relation,” which relates the gravitational waves produced during inflation to the wrinkles in the universe’s curvature. In principle, we can measure this using the hot and cold spots in the CMB or by galaxy surveys. The “toy” inflation models all predict the exact same thing, while the more realistic models with many degrees of freedom can break it. However, we were able to show that a large class of the complicated models actually give a sharp prediction, which becomes more and more precise as we add more complexity to the model (in terms of numbers of quantum fields). This is more evidence that models with lots of knobs and dials can be surprisingly insensitive to their exact settings. Hopefully this means that we only have to know the broad-strokes of the high energy theories in order to get simple answers, similar to our well-studied toy models.
So, I suppose the moral of the story is: even a complicated recipe should still give us a simple cake in the end, and you can tell a simple recipe and a complex recipe apart by looking at the cake!
You can read more here:
L.C. Price, H.V. Peiris, J. Frazer, R. Easther
Gravitational wave consistency relations for multifield inflation
R. Easther, J. Frazer, H.V. Peiris, L.C. Price
Simple predictions from multifield inflationary models
New maps from ESA’s Planck satellite, forming the second major data release (Feb 2015) from the project, have unveiled the ‘polarised’ light from the early Universe across the entire sky, revealing that the first stars formed much later than previously thought. These results are due to the hard work of hundreds of scientists from all over the world! Here we’ll point out some highlights from the new data, focusing in particular on contributions to this huge scientific endeavour made by EarlyUniverse@UCL members!
A major source of information used to piece together the 13.8 billion-year story of the Universe is the cosmic microwave background (CMB) the fossil light resulting from a time when the Universe was hot and dense, only 380,000 years after the Big Bang. Light is polarised when it vibrates in a preferred direction, something that may arise as a result of photons – the particles of light – bouncing off other particles, like electrons. This is exactly what happened when the CMB originated in the early Universe. The CMB light detected by Planck retains a memory of its last encounter with the electrons, captured in its polarisation. The 2015 data release unveils the first high resolution maps of CMB polarisation over the full sky.
The nature of the polarised signal observed by the Planck detectors can be reconstructed with very high precision thanks to the detailed analysis of the polarisation efficiency and spectral measurements performed during ground calibrations by Giorgio Savini.
Planck’s polarisation data confirm the details of the standard cosmological picture determined from its measurement of the CMB temperature fluctuations, but add an important new answer to a fundamental question: when were the first stars born?
As the first stars began to shine, their light interacted with gas in the Universe, and more and more of the atoms were turned back into their constituent particles: electrons and protons. This key phase in the history of the cosmos is known as the ‘epoch of reionisation’. The newly liberated electrons were once again able to collide with the light from the CMB, leaving a tell-tale imprint on the polarisation of the CMB. Planck’s observations of the CMB polarisation now tell us that the first stars formed some 550 million years after the Big Bang – more than 100 million years later than previously thought. This later date on the end of the “Dark Ages” of the Universe implies that it might be easier to detect the very first generation of galaxies with the next generation of observatories, including the James Webb Space Telescope.
New in the 2015 release is the use of high resolution polarisation information of CMB data, providing a powerful and nearly independent test of the temperature-only analysis. The standard cosmological model remains an excellent fit to the data. The data have also enabled new important insights into the early cosmos and its components, including the intriguing dark matter and the elusive neutrinos. In practice, estimating the cosmological parameters requires a statistical framework to confront theory predictions with the data. As a member of the Planck team, Franz Elsner led the development of this analysis pipeline. This task involved the numerical implementation of the algorithm, improving its accuracy, and a comprehensive verification effort on the basis of simulations.
Also new in 2015 is the use of both the anisotropies of the temperature and polarisation of the CMB to reconstruct the entire distribution of the matter from the moment it was emitted 380,000 years after the Big Bang. With extended data Planck has measured, to 2.5% precision, the amplitude of the fluctuations in matter when the Universe was about 3 billion year old. Aurélien Benoit-Lévy contributed to this milestone, as well as creating sky masks that reject the contamination due to foreground emissions that enabled robust cosmological analysis.
The Planck data have delved into the even earlier history of the cosmos, all the way to inflation – the brief era of accelerated expansion that the Universe underwent when it was a tiny fraction of a second old. As the ultimate probe of this epoch, astronomers are looking for a signature of gravitational waves triggered by inflation and later imprinted on the polarisation of the CMB. No direct detection of this signal has yet been achieved. However, when combining the newest all-sky Planck data with the latest results from the BICEP/Keck Collaboration the limits on the amount of primordial gravitational waves are pushed even further down to achieve the best limits yet. As part of this effort Hiranya Peiris tested models of inflation using the latest Planck temperature and polarisation data, searching for tell-tale fingerprints of new physics that operate at the enormous energy scales during inflation.
Einstein’s theory of general relativity tells us about the local curvature of space-time but it cannot tell us about the global topology of the Universe. It is possible that our Universe might have a non-trivial global topology, wrapping around itself in a complex configuration. It is also possible that our Universe might not be isotropic, i.e., the same in all directions. In the 2013 Planck results, some intriguing hints of non-standard geometry were found, suggesting that our Universe might be slightly anisotropic. The Planck 2015 results extended the analysis to include polarisation data for the first time, which provides additional constraining power. These additional data allowed the Planck team including Jason McEwen to strongly rule out the hints of anisotropy seen in the previous analysis. While not a member of the Planck team, Andrew Pontzen computed some of the theoretical predictions that were tested in the analysis. The latest Planck results suggest we live in a Universe with simple topology and geometry, ruling out alternative exotic scenarios and directly testing one of the fundamental assumptions of the standard cosmological model.
You can read more here:
Planck 2015 results. I. Overview of products and scientific results
Planck 2015 results. XIII. Cosmological parameters
Planck 2015 results. XX. Constraints on inflation
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
Planck 2015 results. XV. Gravitational lensing
Planck 2015 results. XVIII. Background geometry and topology of the Universe
We are very excited that our work on simulating cosmic bubble collisions in full General Relativity has been recognised with third place in the inaugural Buchalter Cosmology Prize, announced in January at the 225th meeting of the American Astronomical Society in Seattle, Washington. The annual prize, created by Dr. Ari Buchalter in 2014, seeks to reward new ideas or discoveries that have the potential to produce a breakthrough advance in our understanding of the origin, structure, and evolution of the universe.
Co-author Max Wainwright previously blogged about this work for EarlyUniverse@UCL, and co-authors Hiranya Peiris and Matt Johnson were interviewed by Quanta Magazine for a feature about this work last year. You can find out more about this work in the following video created by the Perimeter Institute!
We are pleased to announce the release of the template maps used in Leistedt and Peiris (2014) and Leistedt, Peiris and Roth (2014). These maps result from projecting the properties of the SDSS photometric images (DR8-10) that are potential sources of systematics for galaxy and quasar clustering studies. An example is given below.
These quantities are all extracted from the FIELDS table in the SDSS database (collecting many useful properties of the SDSS images and fields), and projected using the Mangle software. The resulting maps, released as HEALPix maps at Nside=256 resolution, can be downloaded in the ‘code’ section of this website. If you make use of these maps, please cite the two papers below.
B. Leistedt, H. Peiris, N. Roth
Constraints on primordial non-Gaussianity from 800,000 photometric quasars
This is a multi-verse explanation
of how to constrain models of inflation,
with signals that are seen today
in a large-scale galaxy survey.
We start with a brief repetition
of some concepts, facts and definitions,
because the basis of our current study
is the standard model of cosmology.
The theory of structure formation
is based on inflated quantum fluctuations,
whose amplitudes (for the simplest solution)
should follow a Gaussian distribution.
Any deviation from this simple case
will teach us about physics in a phase
where our Universe was (behold!)
only fractions of fractions of a second old.
A large signal is not expected
and so far remains undetected.
We’ll call this effect PNG,
short for Primordial non-Gaussianity.
The amplitude of PNG
is constrained by the CMB
(the Cosmic Microwave Background),
and these results are pretty sound.
A signal of PNG from inflation
also comes from the galaxy correlation,
for example if the bias deviates
from a constant value on large scales.
And quasars are an ideal candidate:
They’re bright and also strongly correlate
with the dark matter density peaks;
these properties are what one seeks.
The trouble with these observations
is the level of contaminations,
’cause quasars look like stars you see
without detailed spectroscopy.
But for the large volumes that we need
spectroscopic data is highly incomplete.
The sample’s distance and its purity
is thus solely based on photometry.
These systematics often obfuscate
the signal that we try to separate.
And if these effects cannot be mitigated,
no proper values can be estimated.
One solution (the conservative way)
would be to throw some data away,
by masking regions where contaminations
create effects that disagree with expectations.
“But wait” we said, “Oh what a waste
of precious data that can’t be replaced!”
And how can you even know for sure
which part is “wrong” and which is “pure”?
Instead we use for our detection
a method that’s called “mode projection”.
Through clever use of cross-correlations
we clean the data of contaminations.
This process is based on statistics
which makes us highly optimistic:
It won’t just find what you hope to find
(in proper terms: the method’s “blind”)
And so from just one set of data
we get precision that is greater
than what has been obtained before
from two experiments – or even more!
The measured values still permit
a lot of theories that would fit
in addition to the standard one,
so work on this is far from done.
This is the end of our rhyme
we hope you found it worth your time,
and if you are int’rested further
head over to the preprint server.
You can read more here:
B. Leistedt, H. Peiris, N. Roth
Constraints on primordial non-Gaussianity from 800,000 photometric quasars
B. Leistedt, H. Peiris, D. Mortlock, A. Benoit-Lévy, A. Pontzen
Estimating the large-scale angular power spectrum in the presence of systematics: a case study of Sloan Digital Sky Survey quasars
This blog post was written by Andrew Pontzen.
Over this year, a few of us at UCL have been getting increasingly interested in the Lyman alpha forest. It’s a unique probe of how gas is distributed through the universe, made possible by analysing the light from distant, bright quasars. While a lot of emphasis has been placed on the ability of the distribution of gas to tell us about dark energy, we’ve been making the case that there’s more information lurking in the raw data — more here in UCL’s official press release and blog.
For press purposes our work has been illustrated by a picture from an ongoing computer simulation. But actually, one of the neatest aspects of this work is that it can be done with pencil and paper. We’ve built a rigorous framework to study how light propagates through the large-scale universe, without running a conventional simulation. Over the coming months and years we hope to build on that framework to study more about how the large scale universe is reshaped by the light streaming through it.
You can read more here:
UCL press release
What lit up the universe?
A. Pontzen, S. Bird, H. Peiris, L. Verde
Constraints on ionising photon production from the large-scale Lyman-alpha forest
The Lyman-alpha forest
The DESI Collaboration
The DESI Experiment, a whitepaper for Snowmass 2013
Neutrinos: cosmic concordance or contradiction?
Our recent paper on possible new physics in the neutrino sector from cosmological data has been selected as an Editor’s Suggestion in Physical Review Letters! The work was discussed in comprehensive blog posts at phys.org and on the UCL Science Blog; a recent guest post on the topic at Early Universe @UCL is here.
Is the universe a bubble? Let’s check!
The Perimeter Institute did a major press release on our new work in simulating bubble collisions in eternal inflation in full General Relativity. The accompanying video has garnered over 100k views on YouTube! The story was covered in phys.org and IFLScience. A guest post on this topic was previously featured on Early Universe @UCL.
This guest blog post was written by Stephen Feeney.
The cosmic microwave background (CMB) forms the cornerstone of the concordance cosmological model, ΛCDM, providing the largest and, arguably, cleanest-to-interpret picture of our Universe currently available; however, this model is buttressed on all sides with measurements of cosmologically relevant quantities derived using a huge variety of other astrophysical objects. Examples include:
the local expansion rate of the Universe (i.e., the constant in Hubble’s Law relating the distance of an object and its recession speed), measured using so-called standard candles — things we (think we!) know the inherent brightness of — such as Cepheid variable stars and Type Ia supernovae;
the age of the Universe, which must be greater than the ages of the oldest things we can see, like globular clusters and metal-poor stars; and
the shape or amplitude of the matter power spectrum, i.e., how much matter, (both normal and dark) is bound up in structures of different sizes. This can be measured in a number of different ways, including galaxy surveys, weak-gravitational-lensing surveys (which exploit the fact that matter bends the path of light, and hence changes the shape of faraway objects, to “weigh” the Universe) and counts of galaxy clusters.
Using our cosmological model, we can extrapolate our CMB observations — observations of the Universe when it was only 400,000 years old — to predict how quickly we think the Universe should be expanding now (billions of years later), how old it should be, and how many galaxy clusters we should see of a given mass. If our model of cosmology (and crucially astrophysics — more on this below) is correct, and we truly understand our instruments, then all of our measurements should agree with the CMB predictions. Conversely, if our measurements don’t agree then we might have something wrong! With releases of stunning new cosmological data popping up more regularly than a London bus — ain’t being a 21st century cosmologist great? — there’s no time like the present to ask just how concordant is our concordance model?
Now, the first thing to note is that our measurements very nearly do agree. Let’s take the expansion rate as an example. Extrapolating the Planck satellite’s CMB observations to the present day, we expect that the expansion rate should be 67.3 ± 1.2 km/s/Mpc (the slightly funky units reduce to 1/s, the same as any old rate). The Hubble Space Telescope’s dedicated mission to measure this quantity, which used observations of some 600 Cepheid variables and over 250 supernovae, concluded that the expansion rate is 73.8 ± 2.4 km/s/Mpc. The level of agreement between these two values is pretty mind-blowing, particularly when you consider we’re talking about modelling a few billion years of cosmological evolution. We’re comparing predictions based on observations of the Universe when it was a soup of photons, protons, electrons, a few alpha particles and not much more to measurements of pulsating and exploding stars! Put simply: it looks like we’re doing a good job!
When we compare the difference between these two values with the errors on the measurements, however, things look a little less rosy. Even though the values are close, their error-bars are now so small that this level of disagreement indicates we don’t understand something important, either about the data or the model. Or, of course, both. Looking elsewhere, we see similar issues popping up. Though our measurements of the age of the Universe look ok compared to the CMB predictions, estimates of the amount of matter from cluster counts (and weak-lensing measurements) suggest that there isn’t as much small-scale (cosmologically speaking) structure as we’d expect from extrapolating the CMB.
So far, so mysterious. Luckily though there are (plenty of!) models waiting to explain the discrepancy. What we’re looking for here are processes that can make the current Universe deviate from the predictions of the early Universe, things like massive neutrinos, dark energy and the like, whose effects only show up once the Universe has reached a certain age. Massive neutrinos have been receiving a lot of attention recently, with several papers reporting tentative detections of the existence of an additional massive sterile neutrino species (“sterile” here meaning that the neutrinos don’t even interact via the weak nuclear force: these are some seriously snooty particles…). Where does the evidence for these claims come from? Well, the effects of sterile neutrinos on cosmology can be described by their temperature and mass, which govern when the neutrinos are cool enough to stop behaving like radiation (pushing up the expansion rate and damping small-scale power) and instead start behaving like warm dark matter. Warm dark matter, unlike its cold cousin, moves too quickly to cluster on small scales, and thus suppresses the formation of cosmological structure. If a population of sterile neutrinos was produced in the Big Bang, and it became non-relativistic after the CMB was formed, the matter power spectrum on these scales would be smaller than that predicted by the CMB.
Okay, so it looks like an extra sterile neutrino could explain the paucity of clusters in the Universe. Nobel Prizes all round! Except that’s not the whole story. A Universe with three normal neutrino species and an extra sterile one should have a low Hubble expansion rate as well as low cluster counts: that is not what is observed. Quite the opposite, in fact, as we’ve seen: a range of local measurements of the Hubble constant point to a value higher than expected. Thus, it appears that the sterile neutrino model does not provide the new concordance we all crave. This point has been very nicely illustrated in a recent paper by Boris, Hiranya and Licia, who demonstrate (using the data mentioned above and more) that adding a sterile neutrino to the standard cosmological model can not reconcile the high local measurement of the Hubble rate and the low cluster counts with the predictions of higher-redshift data from CMB observations (which by themselves don’t seem to want anything to do with massive neutrinos). In scientific terms, the datasets remain in tension, and we all know what happens when we combine data that are in tension: if there is only a small overlap between the conclusions of each dataset, we end up with artificially small ranges of allowed parameter values.
What else could explain the discrepancy then? Well, firstly and most excitingly, we could have the wrong model. Perhaps there is another physical process taking place on cosmological scales that perfectly predicts all of our observables. If this is the case, this is where Bayesian model selection comes into its own: once we have the predictions of this model, we can easily test whether the model or its competitors is most favoured by the data. (Of course, Bayesian model selection already has a part to play: it’s a more naturally cautious method than parameter estimation, and even using the current data in tension it shows that the sterile neutrino model isn’t favoured over ΛCDM.)
The other possibility is that there are undiagnosed systematic errors in one or more of the datasets involved. This is not an outlandish possibility (and historically this is where confirmation bias raises its ugly head): the measurements we’re discussing here are all hard to do, and are rarely free from interference from astrophysical contaminants. It’s very easy to only focus on the cosmological quantities derived from these observations, and just chuck them into your analysis as a number with some error-bars, but it’s important to remember that each of these numbers is itself the distillate of a complicated astrophysical whodunit. Like detectives using clues and logic to piece together the most likely story of what happened, we use observations and physical theory to figure out the most probable values of the cosmological parameters. The values of the parameters therefore depend on how well we understand both our data and the objects we observe. Measurements of the local expansion rate rely on standard candles: we need to understand the physical processes that determine the brightness of these objects, and how dust or metals in their surroundings might affect that brightness. To derive measurements of the matter power spectrum we need to understand how galaxies (and not only galaxies in general, but the specific ones we see in our surveys) map onto the dark matter distribution, how all of this evolves as structures collapse under gravity, how the amount of X-rays emitted by a cluster relates to its mass, how the shapes of galaxies are warped by intervening matter (and are distributed in the first place!). For age measurements we need to understand how stars evolve and impact the formation of new stars in their surroundings, etc., etc. Are we sure, for example, that our conversion from cluster counts (or the amount of X-rays radiated by clusters) into the amplitude of the matter power spectrum is exactly correct? How confident are we that the standard candles used to measure the local expansion rate are truly standard (i.e. could variations in these objects mean some are actually inherently brighter than others), or that the calibrations between different candles are correct? And what if our understanding of the instruments aboard the Planck satellite is not perfect? Tweaking any one of these could cause our measurements of the cosmological parameters to shift (and in any direction: there’s no guarantee they will move into agreement!). We need to dig around our data to determine whether any instruments are misbehaving, and test both the physical principles and statistical tools used to convert our data into constraints on cosmological parameters to be sure that this isn’t the source of the discrepancy.
So, this is where we find ourselves today. It seems recently that everyone’s re-examining everyone else’s data: the expansion rate calculations have been revisited by Planck people, and the Planck power spectrum analysis has been tweaked by WMAP people, each potentially resulting in small but important shifts in parameter values. And the good news is that no punches are being thrown (yet!). I find this to be very cool, and very exciting: we’re not all sitting here agreeing; neither are we all flatly claiming our data are error-free; nor are we blindly accepting that claims of new physics are true, as awesome as it would be if they were. The next year or so, in which these re-examinations are in turn examined and, more importantly, new temperature and polarisation data from the Planck satellite appear, will subject our cosmological models to extremely exacting scrutiny to truly determine whether concordance, be it new or old, can be found.
You can read more here:
Planck 2013 Results. XVI. Cosmological Parameters
H. Bond, E. Nelan, D. VandenBerg, G. Schaefer and D. Harmer
HD 140283: A Star in the Solar Neighborhood that Formed Shortly After the Big Bang
R. Battye and A. Moss
Evidence for Massive Neutrinos from CMB and Lensing Observations
C. Dvorkin, M. Wyman, D. Rudd and W. Hu
Neutrinos Help Reconcile Planck Measurements with Both Early and Local Universe
B. Leistedt, H. Peiris and L. Verde
No New Cosmological Concordance with Massive Sterile Neutrinos
S. Feeney, H. Peiris and L. Verde
Is There Evidence for Additional Neutrino Species from Cosmology?
D. Spergel, R. Flauger and R. Hlozek
Planck Data Reconsidered
This blog post was written by Marc Manera.
More than one million galaxies have been observed in the last three years by the 2.5 meter telescope at the Apache Point Observatory in New Mexico. In the picture above you can see the telescope (and me) just before sunset during a visit I made to the observatory some years ago. Some of the astronomers and cosmologists of the Sloan Digital Sky Survey had met nearby to discuss the science that can be done with the forthcoming observations – but now the data are already here.
When you have observations of the position and colour of more than one million galaxies at your fingertips, there are a lot of questions about the universe that can be investigated. In this post I will focus on how we have measured the expansion of the universe using the distribution of galaxies from the BOSS survey, which is part of the Sloan Digital Sky Survey.
BOSS – the Baryon Oscillation Spectroscopic Survey – has targeted 1.35 million galaxies covering approximately 10,000 square degrees. Galaxies are observed by setting optical fibres in the focal plane of the telescope. The light of each galaxy is then carried to a spectrograph where it is diffracted into a spectrum of wavelengths or frequencies i.e. colours – like a rainbow – and the data are stored.
As the light travels from the galaxy where it was originally emitted to us, the spectrum of colours of the galaxies shifts towards the red; i.e., the galaxies appear “redder” than their original colour. We call this change in colour redshift, and we can measure it because we know the colour/frequency of a particular atomic transition as it would have been observed in the galaxies when it was emitted. The magnitude of the colour change – the redshift – is an important cosmological quantity, and tells us how much the universe has changed in size since that light was emitted. If the universe has doubled its volume since then, then the wavelength of the light that we observe will have doubled too.
The figure above shows slices through the SDSS 3-dimensional map of the distribution of galaxies. The Earth is at the centre, and each point represents a galaxy, typically containing about 100 billion stars. The outer circle is at a distance of 2 billion light years. The wedges showing no galaxies were not mapped by the SDSS because dust in our own Galaxy obscures the view of the distant universe in this direction. Both slices contain all galaxies between -1.25 and 1.25 degrees declination.
As the SDSS map shows, galaxies in the universe are not distributed randomly. Galaxies tend to cluster in groups of galaxies because they attract each other through gravity. Galaxies also have a particular separation at which they are more likely to be found; this separation is set by plasma physics – it is the Baryon Acoustic Oscillation characteristic distance – and we know it is about 4.5 x 1021 km. This is the distance that galaxies “like” to keep between themselves, in a typical sense.
In the sky, for each set of galaxies that emitted their light at a particular moment during the expansion of the universe, the typical separation of the galaxies subtends a particular angle. Since we can calculate this separation between galaxies from physics (r) and the angle it subtends by observation (θ), using the basic geometry of a triangle we can work out the distance between us and these galaxies (d). This is illustrated in the final figure below.
Finally, because the speed of light in constant, we know how long ago the light from the galaxies was emitted, and thus we have all the information we need to deduce the expansion history of the universe.
So to sum up, to work out the expansion rate of the universe we select several samples of galaxies; each sample will have emitted its light at a different time, and therefore it is at a different distance to us. We can measure this distance using simple geometry by observing the typical angle by which galaxies are separated. Once we have the distance to each sample of galaxies, we also have a measure of how long ago they emitted that light. Now, from the colours of the galaxies (the redshift) we also know how big the universe was at that time. For each set of galaxies we know the age of the universe at a particular moment and how big the universe was at that time. We have therefore determined the expansion history of the universe.
This is exactly what the BOSS survey has done using three sets of galaxies at different distances.
You can read more here:
L. Anderson, E. Aubourg, S. Bailey et al (BOSS collaboration paper)
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples
This guest blog post was written by Layne Price.
The cosmological principle says that our universe looks the same regardless of where we are or in which direction we look. Obviously, a universe that exactly satisfies this principle is unimaginably boring, precisely because we wouldn’t be here to imagine it. In fact, a quick measurement using my bathroom scale and a tape measure suggests that I have a density around 1100 kg/m3, which is 1030 times larger than the cosmological average. Clearly, the universe is homogeneous and isotropic only when averaged over large-enough scales. So, where do the local differences in density come from?
Enter inflation. This is a class of theories that uses the inherent randomness of quantum perturbations to generate local fluctuations in the dominant energy component of the primordial universe: hypothesized quantum fields with no intrinsic spin. Fields of this type are called scalars and show up often in physics: phonons in solid state physics are scalars, as is the recently discovered Higgs boson. The random fluctuations in these scalar fields cause small changes in the spacetime curvature, collecting dark matter and baryons into regions of space which eventually collapse into galaxies, stars, and people.
Although the local curvature perturbations are random, not all randomness is equal. The different possible variances of the random curvature perturbations are distinguishable through the shape of the acoustic peaks in the angular power spectrum of the cosmic microwave background (CMB). For example, if the perturbations were pure Gaussian white noise, then there would be more power on smaller angular scales than has been seen by the WMAP and Planck satellites. This simple type of randomness has now been eliminated at a level greater than 5 sigma.
Interestingly, inflation predicts a small, but non-negligible deviation from white Gaussian noise, which is exactly what we see. However, the amount and type of this deviation depends on the way the scalar field theory is constructed — and there are lots of ways to make scalar field theories. If there is only one scalar field, there is usually only one way to inflate: one field using its potential energy to drive the universe’s expansion, which in turn acts as a frictional force to stop the field from gaining too much momentum. This causes a runaway effect where the expansion becomes progressively faster, sustaining inflation for an extended period of time. Since single-field models depend only on the potential energy of one field, for every potential energy function there is usually a unique prediction for the statistics of the CMB.
However, fundamental particle physics theories, like string theory or supersymmetry, often have hundreds or thousands of scalar fields. Since these theories become most relevant at energy scales close to the inflationary energy scale, there is considerable interest in analyzing their dynamics. This certainly complicates things. Multifield models have not only one, but usually an infinite number of ways to inflate. The potential energy that drives inflation can now be distributed across any combination of the fields and this distribution of energy changes during the inflationary period in complicated ways that depend on the fields’ initial conditions. The dynamics can even be chaotic! With so many more degrees of freedom, multifield models give a much wider range of possible universes. Understanding whether or not our universe fits into this spectrum is obviously a big challenge!
To determine the predictions of multifield models it is therefore useful to employ a numerical approach that can handle their increased complexity. Over a few visits back-and-forth between London and Auckland, my collaborators and I have built an efficient numerical engine that can solve the exact equations describing the inhomogeneous perturbations. The speed of the code has allowed us to calculate statistics for models with over 200 scalar fields — many more than previously possible. Perhaps surprisingly, our calculations indicate that the most likely predictions of the multifield models are bunched tightly around tiny regions of parameter space and are not sensitively dependent on the initial conditions of the fields.
This is important because, in order to calculate how much the observations favor a given model, we need to sample the entire relevant portion of the model’s parameter space and weight each combination of parameters according to how well they fit our CMB observations. This process is computationally difficult, so if we can argue that the fields’ initial conditions only weakly affect the model’s predictions, then it allows us to use a smaller sample, greatly simplifying the calculation.
The end-goal of this line of research is to know which animal in the zoo of inflation models, if any, gives the best description of our universe. For each of these models we must individually calculate the probability that the model is true given the data we have extracted from the CMB — in Bayesian statistics this is known as the posterior probability for the model. By taking the ratio of two models’ posterior probabilities we can determine which model we should bet on being the better description of nature. While we still have more work to do before we can calculate which multifield inflation model is best, we now have many efficient tools in place. There will be much more to come soon!
You can read more here:
R. Easther, J. Frazer, H. V. Peiris, and L. C. Price
Simple predictions from multifield inflationary models
R. Easther and L. C. Price
Initial conditions and sampling for multifield inflation
The scientists working on Planck have been awarded a Physics World Top 10 breakthrough of 2013 “for making the most precise measurement ever of the cosmic microwave background radiation”.
The European Space Agency’s Planck satellite is the first European mission to study the origins of the universe. It surveyed the microwave sky from 2009 to 2013, measuring the cosmic microwave background (CMB), the afterglow of the Big Bang, and the emission from gas and dust in our own Milky Way galaxy. The satellite performed flawlessly, yielding a dramatic improvement in resolution, sensitivity, and frequency coverage over the previous state-of-the-art full sky CMB dataset, from NASA’s Wilkinson Microwave Anisotropy Probe.
The first cosmology data from Planck was released in March 2013, containing results ranging from a definitive picture of the primordial fluctuations present in the CMB temperature, to a new understanding of the constituents of our Galaxy. These results are due to the extensive efforts of hundreds of scientists in the international Planck Collaboration. Here we focus on critical contributions made at UCL to these results.
Planck’s detectors can measure temperature differences of millionths of a degree. To achieve this, some of Planck‘s detectors must be cooled to about one-tenth of a degree above absolute zero – colder than anything in nature – so that their own heat does not swamp the signal from the sky. Giorgio Savini spent the five years prior to launch building the cold lenses as well as testing and selecting all the other optical components which constitute the “eyes” of the Planck High Frequency Instrument. During the first few months of the mission he helped to analyze the data to make sure that the measurements taken in space and the calibration data on the ground were consistent.
UCL researchers Hiranya Peiris, Jason McEwen, Aurélien Benoit-Lévy and Franz Elsner played key roles in using the Planck cosmological data to understand the origin of cosmic structure in the early universe, the global geometry and isotropy of the universe, and the mass distribution of the universe as traced by lensing of the CMB. As a result of Planck’s 50 megapixel map of the CMB, our baby picture of the Universe has sharpened, allowing the measurement of the parameters of the cosmological model to percent precision. As an example, Planck has measured the age of the universe, 13.85 billion years, to half per-cent precision.
The precision of the measurements has also allowed us to rewind the story of the Universe back to just a fraction of a second after the Big Bang. At that time, at energies about a trillion times higher than produced by the Large Hadron Collider at CERN, all the structure in the Universe is thought to have been seeded by the quantum fluctuations of a so-called scalar field, the inflaton. This theory of inflation predicts that the power in the CMB fluctuations should be distributed as a function of wavelength in a certain way. For the first time, Planck has detected, with very high precision, that the Universe has slightly more power on large scales compared with small scales – the cosmic symphony is very slightly bass-heavy, yielding a key clue to the origin of structure in the Universe. Inflation also predicts that the CMB fluctuations will have the statistical properties of a Gaussian distribution. Planck has verified this prediction to one part in 10,000 – this is the most precise measurement we have in cosmology.
As the CMB photons travel towards us their paths get very slightly bent by massive cosmological structures, like clusters of galaxies, that they have encountered on the way. This effect, where the intervening (dark) matter acts like a lens – only caused by gravity, not glass – on the photons, slightly distorts the CMB. The Planck team was able to analyse these distortions, extract the lensing signature in the data, and create the first full-sky map of the entire matter distribution in our Universe, through 13 billion years of cosmic time. A new window on the cosmos has been opened up.
Einstein’s theory of general relativity tells us about the local curvature of space-time but it cannot tell us about the global topology of the Universe. It is possible that our Universe might have a non-trivial global topology, wrapping around itself in a complex configuration. It is also possible that our Universe might not be isotropic, i.e., the same in all directions. The exquisite precision of Planck data allowed us to put such fundamental assumptions to the test. The Planck team concluded that our Universe must be close to the standard topology and geometry, placing tight constraints on the size of any non-trivial topology; some intriguing anomalies remain at the largest observable scales, requiring intense analysis in the future.
Aside from additional temperature data not included in the first year results, the upcoming Planck data release in summer 2014 will also include high resolution full-sky polarization maps. This additional information will not only allow us to improve our measurements of the cosmological parameters even further; it will also advance our understanding of our own Galaxy by probing the structure of its magnetic fields and the distribution and composition of dust molecules. There is a further, exciting possibility: if inflation happened, the structure of space should be ringing with primordial gravitational waves, which can be detected in the polarized light of the CMB. We may be able to detect these in the Planck polarization data.
This guest blog post was written by Max Wainwright.
In modern cosmological models, the very, very early Universe was dominated by a period of exponential growth, known as inflation. As inflation stretched and smoothed the expanding space, particles that were once right next to each other would soon find themselves at the edges of each other’s cosmological horizons, and after that they wouldn’t be able to see each other at all. It was a time of little matter and radiation — an almost complete void except for the immense vacuum energy that drove the expansion.
Luckily, at some point inflation stopped. The vacuum energy decayed into a hot dense plasma soup, which would later cool into particles and, by gravitation, conglomerate into all of the complicated cosmic structure that we see today.
The theory of eternal inflation is quite similar: the very early Universe was dominated by exponential growth, and at some point the growth needed to stop and the energy needed to be converted into matter and radiation. The difference is that in eternal inflation, the growth need not have stopped all at once. Instead, little bubbles of space could have randomly stopped inflating, or fallen onto trajectories which would lead to inflation’s end. The bubbles’ interiors would be in a lower energy state (less vacuum energy means slower inflation), and since they’re in an energetically favorable state they would expand into the inflating exterior. This is much the same as little bubbles of steam growing and expanding in a pot of boiling water: a steam bubble nucleates randomly, and then grows by converting water into more steam. If the Universe weren’t expanding, or if it were expanding slowly, each bubble would eventually run into another bubble and the entire Universe would be converted to the lower vacuum energy. But, in a rapidly expanding universe, the space between bubbles is growing even as the bubbles are themselves growing into that space. If the expansion is fast enough, the growth of inflating space will be faster than its conversion into lower-energy bubbles — inflation will never end.
Signals and Bubble Collisions
Eternal inflation is therefore a theory of many bubble universes individually nucleating and growing inside an ever-expanding background multiverse. If true, eternal inflation would mean that everything that we see, plus a huge amount that we don’t see (hidden behind our cosmological horizon), all came from a single bubble amongst an infinity of other bubbles. Eternal inflation takes the Galilean shift one step further: not only are we not the center of the Universe, but even our universe isn’t the center of the Universe! But how can we ever hope to test this theory?
Most pairs of bubble universes will never collide with each other — they’re too far apart, and the space between them is expanding too fast — but some pairs will form close enough together that they will meet. The ensuing collision will perturb the space-time inside each bubble, and, if we’re lucky, that perturbation may be visible today as a small temperature anisotropy in the cosmic microwave background (CMB).
In a recent paper with my collaborators (M. Johnson, H. Peiris, A. Aguirre, L. Lehner, and S. Liebling) we examined such a possibility. We developed a code that, for the first time, is able to simulate the collision of two bubble universes and follow their evolution all the way to the end of inflation inside each bubble. We then computed the space-time as seen by an observer inside one of the bubbles, and found what the collision would look like on his or her sky.
The model that we use starts with potential energy as a function of a single scalar field. There is a little bump at the top of the potential, forming a local minimum and a barrier. If the field is in the minimum, then it would classically stay there forever. But quantum mechanically the field can tunnel across the barrier — this is the start of a bubble universe. The field inside the bubble will then slowly roll down the potential. The interior will inflate (which is important for matching with standard cosmology), but at a slower rate than the exterior. Once the field reaches the potential’s absolute minimum and the vacuum energy goes to zero, inflation will stop and the kinetic energy in the field will convert into the hot plasma mentioned above (a process known as ‘reheating’).
This next figure shows a simulation of a single collision. By symmetry, we only need to simulate one spatial dimension along with the time dimension. The x-axis is the spatial dimension, and the y-axis shows elapsed time (the time-variable N measures the number of e-folds in the eternally inflating vacuum. That is, it measures how many times the vacuum has grown by a factor of e). With our funny choice of coordinates, there is exponentially more space as we go up the graph, so even though it looks like the bubbles asymptote to a fixed size they are physically always getting bigger. You can see that collision can have a drastic effect upon the interior of the bubbles! In this case, the effect is to push the field further down the inflationary potential.
With a collision simulation in hand, we could then figure out what collision actually looks like to an observer residing inside one of the bubbles. This step was pretty complicated — it involved a few tricky coordinate transformations and building up the observer space-time by combining many geodesic trajectories — but the end result was a measure of the comoving curvature perturbation R, which, by the Sachs-Wolfe approximation, is directly proportional to the temperature anisotropy signal that an observer would see in the CMB. The next figure shows a slice of the perturbation across an observer’s coordinates.
Predictions and Next Steps
What I’ve shown here is the result of a single bubble collision for a single observer, but, as shown in the paper, we ran many different collisions with different initial separations between bubbles, and found the resulting signal for many different observers. This allowed us to make robust predictions for what sizes and shapes of collisions we should expect to see, given this model. We will then use this information to actually hunt for the collision signals in the sky using data from the Planck space observatory.
So far we’ve only examined one model for how the scalar-field potential should look, but we have no strong theoretical bias to believe that that model is right. Now that we have all of the machinery, we can start examining a slew of different models with different collision properties. Will the collisions generically look the same, or will different models predict very different signals? If we find a signal, what models can it rule out?
It’s an exciting time to be a cosmologist. If we’re lucky, we may soon learn of our proper place in the multiverse.
You can read more here:
C. L. Wainwright, M. C. Johnson, H. V. Peiris, A. Aguirre, L. Lehner, S. L. Liebling
Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity
M. C. Johnson, H. V. Peiris, L. Lehner
Determining the outcome of cosmic bubble collisions in full General Relativity
S. M. Feeney, M. C. Johnson, J. D. McEwen, D. J. Mortlock, H. V. Peiris
Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background
This blog post was written by Andrew Pontzen and originally published by astrobites. Hiranya Peiris will be writing a response exploring why she believes that both rapid and slow expansion are confusing, and giving her take on explaining the inflationary picture to non-specialists – watch this space!
A tale of two universes
There are many measurements which constrain the history of the universe. If, for example, we combine information about how fast the universe is expanding today (from supernovae, for example) with the known density of radiation and matter (largely from the cosmic microwave background), we pretty much pin down how the universe has expanded. An excellent cross-check comes from the abundance of light elements, which were manufactured in the first few minutes of the universe’s existence. All-in-all, it’s safe to say that we know how fast the universe was expanding all the way back to when it was a few seconds old. What happened before that?
Assuming that the early universe contained particles moving near the speed of light (because it was so hot), we can extrapolate backwards. As we go back further in time, the extrapolation must eventually break down when energies reach the Planck scale. But there’s a huge gap between the highest energies at which physics has been tested in the laboratory and the Planck energy (a factor of a million billion or so higher). Something interesting could happen in between. Inflation is the idea that, because of that gap, there may have been a period during which the universe didn’t contain particles. Energy would instead be stored in a scalar field (a similar idea to an electric or magnetic field, only without a sense of direction). The Universe scales exponentially with time during such a phase; the expansion rate accelerates. (Resist any temptation to equate ‘exponential’ or ‘accelerating’ with ‘fast’ until you’ve seen the graphs.) Ultimately the inflationary field decays back to particles and the classical picture resumes. By definition, all is back to normal long before the universe gets around to mundane things like manufacturing elements. For our current purposes, it’s not important to see whether inflation is a healthy thing for a young universe to do (wikipedia lists some reasons if you’re interested). We just want to compare two hypothetical universes, both as simple as possible:
- a universe containing fast-moving particles (like our own once did);
- as (1), but including a period of inflation.
Comparisons are odorous
There are a number of variables that might enter the comparison:
- a: the scalefactor, i.e. the relative size of a given patch of the universe at some specified moment;
- t: the time;
- da/dt: the rate at which the scalefactor changes with time;
- or if you prefer, H: the Hubble rate of expansion, which is defined as d ln a / dt.
We’ll take a=1 and t=0 as end conditions for the calculation. There’s no need to specify units since we’re only interested in comparative trends, not particular values. There are two minor complications. First, what do we mean by ‘including inflation’ in universe (2)? To keep things simple it’ll be fine just to assume that the pressure in the universe instantaneously changes. (Click for a slightly more specific description.) The change will kick in between two specified values of a — that is, over some range of ‘sizes’ of the universe. In particular, taking the equation of state of the universe to be pressure = w × density × c2, we will assume w=1/3 except during inflation, when w= –1. The value of w will switch instantaneously at a=a0, and switch back at a=a1. (Click for details of the transition.)The density just carries over from the radiation to the inflationary field and back again (as it must, because of energy-momentum conservation). In reality, these transitions are messy (reheating at the end of inflation is an entire topic in itself) – but that doesn’t change the overall picture.
Finding the plot
The Friedmann equations (or equivalently, the Einstein equations) take our history of the contents of the universe and turn it into a history of the expansion (including the exponential behaviour during inflation). But now the second complication arises: such equations can only tell you how the Hubble expansion rate H (or, equivalently, da/dt) changes over time, not what its actual value is. So to compare universes (1) and (2), we need one more piece of information – the expansion rate at some particular moment. Since we never specified any units, we might as well take H=1 in universe (1) at t=0 (the end of our calculation). Any other choice is only different by a constant scaling. What about universe (2)? As discussed above, the universe ends up expanding at a known rate, so really universe (2) had better end up expanding at the same rate as universe (1). But, for completeness, you’ll be able to modify that choice below and have universe (1) and (2) match their expansion rate at any time. All that’s left is to choose the variables to plot. I’ve provided a few options in the applet below. It seems they all lead to the conclusion that inflation isn’t ultra-rapid expansion; it’s ultra-slow expansion. By the way, if you’re convinced by the plots, you might wonder why anyone ever thought to call inflation rapid. One possible answer is that the expansion back then was faster than at any subsequent time. But the comparison shows that this is a feature of the early universe, not a defining characteristic of inflation. Have a play with the plots and sliders below and let me know if there’s a better way to look at it.
This plot shows the Hubble expansion rate as a function of the size of the universe. A universe with inflation (solid line) has a Hubble expansion rate that is slower than a universe without (dashed line). Inflation is a period of slow expansion! In the current plot, sometimes the inflationary universe (solid line) is expanding slower, and sometimes faster than the universe without inflation (dashed line). But then, you’ve chosen to make the Hubble rate exactly match at an arbitrary point during inflation, so that’s not so surprising. Currently it looks like the inflationary universe (solid line) is always expanding faster than the non-inflationary universe (dashed line). But the inflationary universe ends up (at a=1) expanding much faster than H=1, which was our target based on what we know about the universe today. So there must be something wrong with this comparison.
This plot shows the size of the universe as a function of time. Inflationary universes (solid line) hit a=0 at earlier times. In other words, a universe with inflation (solid line) is always older than one without (dashed line) and has therefore expanded slower on average. Inflation is a period of slow expansion! With the current setup you’re not matching the late-time expansion history in the inflationary universe against the known one from our universe; to make a meaningful comparison, the dotted and solid lines must match at late times (t=0). So the plot can’t be used to assess the speed of expansion during inflation.
This plot shows the Hubble expansion rate of the universe. The universe with an accelerating period (solid line) is always expanding at the same rate or slower than the one without (dashed line). Inflation is a period of slow expansion! Currently it looks like the inflationary universe (solid line) may expand faster than the non-inflationary universe (dashed line). But the inflationary universe ends up (at t=0) expanding much faster than H=1, which was our target based on what we know about the universe today. So there must be something wrong with this comparison.
This plot shows the rate of change of scalefactor (da/dt) as a function of time before the present day. The universe with an accelerating period (solid line) is always expanding at the same rate or slower than the one without (dashed line). Inflation is a period of slow expansion! With the current setup you’re not matching the late-time expansion history in the inflationary universe (solid line) against the known one from our universe (da/dt does not match at t=0, for instance). So the plot can’t be used to assess the speed of expansion during inflation.
First select the range of scalefactors over which inflation occurs by dragging the two ends of the grey bar. Currently, a0=X and a1=X
In realistic models of inflation, this range would extend over many orders of magnitude in scale, making the effects bigger than the graphs suggest.
Now select the scalefactor at which the expansion rate is matched between universe (1) and (2).
At the moment amatch=X: you’re matching after inflation is complete. That makes sense because various observations fix the expansion rate at this time.
At the moment amatch=X: you’re matching before or during inflation. Look at the Hubble rate at the end of inflation and you’ll find it disagrees between the two universes. That means they can’t both match what we know about the universe at late times, so the comparison isn’t really going to be fair.