*This blog post was written by Aurélien Benoit-Lévy.*

In my previous post, I mentioned CMB lensing and said that it was going to be a big thing. And indeed, CMB lensing has been presented as one of the main scientific results of the recent data release from the Planck Collaboration. So what is CMB lensing? Put succinctly, CMB lensing is the deflection of CMB photons as they pass clumps of matter on the way from the last scattering surface to our telescopes. These deflections generate a characteristic signature in the CMB that can be used to map out the distribution of all of the matter in our Universe in the direction of each incoming photon. Let me now describe these last few sentences in greater detail.

I am sure you are familiar with images of distorted and multiply-imaged galaxies observed around massive galaxy clusters. All of these images are due to the bending of light paths by changes in the distribution of matter, an effect generally known as gravitational lensing. The same thing happens with the CMB: the trajectories of photons coming from the last scattering surface are modified by gradients in the distribution of matter along the way: i.e. the large-scale structure of our Universe.

The main effect is that the CMB we observe is sightly modified: the temperature we measure in a certain direction is actually the temperature we would have measured in a slightly different direction if there were no matter in the Universe. These deflections are small — about two arcminutes, or the size of a pixel in the full-resolution Planck map — and can hardly be distinguished by eye. Indeed, if you look at the nice animation by Stephen Feeney, it not possible to say which is the lensed map and which is the unlensed map. But there’s one thing we can see, and that’s that the deflections are not random. If you concentrate on one big spot (either blue or red) you’ll see that it moves coherently in one single direction. The coherence of these arcminute deflections over a few degrees is extremely important as it enables us to estimate a quantity known as the lensing potential: the sum of all the individual deflections experienced by a photon as it travels from the last scattering surface. Although we can only measure the net deflection, rather than the full list of every deflection felt by the photon, the lensing potential still represents the deepest measurement we can have of the matter distribution as it probes the whole history of structure formation!

Now, how can we extract this lensing potential from a CMB temperature map? As I mentioned earlier, CMB lensing generates small deflections (a few arcminutes) but correlated on larger scales (a few degrees). This mixing of scales (small and large) results from small non-Gaussianities induced by CMB lensing. More precisely, the CMB temperature and its gradient become correlated, and this correlation is given precisely by the lensing potential. We can therefore measure the correlation between the temperature and the gradient of a CMB map to provide an estimate of the lensing potential. Of course, this operation is not straightforward and there are quite a lot of complications due to the fact that the data are not perfect. But we can model all of these effects, and, as they are largely independent of CMB lensing, they can be easily estimated using simulations and then simply removed from the final results.

It’s as simple as that! However, there’s much more still to come as I haven’t yet spoken of the various uses of this lensing potential! But that’s another story for another time…