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Gravitational lensing and CMB photons

I wanted answers to two questions at the beginning of the semester, both of which are related to general relativity and cosmology. Both of the questions are related to gravitational lensing, a phenomenon where light bends around massive objects. Gravitational lensing was one of the predictions of Einstein's General theory of relativity and was observed during a solar eclipse.

The first of my questions is related to how distant galaxies are lensed by galaxy clusters in our line of sight. Conventional optics governs that if two sources of light are placed behind one another, the farther one will be obscured by the closer one. General relativity, on the other hand, allows for light emitted by the distant source to get bent around the closer source to reach us. It has been observed to happen that multiple images of the distant galaxy are formed due to a lens in the line of sight. Einstein's cross is one such example. Now, having covered the topics of curvature and geodesics in the course on general relativity and cosmology, I want to understand the equations that govern bending of light and I want to learn how to model the lens given the number of images observed or how to understand the images given a lens model.

Secondly, I want(ed) to know if CMB photons are lensed by galaxy clusters too. Galaxy clusters give raise to some interesting phenomenon, such as the Sunyaev-Zel'dovich Effect, which is an inverse compton effect. I wanted to know if such CMB photons would also be effected in such a fashion. And apparently they do. SPT, ACT and now Planck have released data sets pertaining to lensing of CMB photons by massive clusters. I'd like to dig a bit deeper into this to understand exactly how this is quantified, at various angular scales.

While searching for literature on the CMB lensing, I came across another interesting effect on CMB due to clusters. One can imagine galaxy clusters as potential wells or potential hills through which the CMB photons have to pass. In a static world, a photon would have the same energy before and after the cluster/well/hill but because we live in an expanding world, there is a slight difference in energy before and after the well/hill. This is referred to as the Sachs-Wolfe effect.

The more I dig, the more it seems that astronomy (technically cosmology) gets really interesting on the extremely large scales.

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