# CMB anisotropy

### Problem 1

problem id: per25

Obtain the equation of motion for photon in metrics ($ds^2=a^2(\eta)[(1+2\Phi)d\eta^2-(1-2\Phi)\delta_{ij}dx^idx^j]$) in linear approximation in $\Phi$.

### Problem 2

problem id: per26

For the Universe, dominated by a substance with equation of state $p = w \rho$, connect in the first approximation the fluctuations of the gravitational potential of the CMB with $\Phi$.

### Problem 3

problem id:

Estimate the spatial scale of Silk effect. Assume that at the temperatures we are interested in, photon changes direction randomly, and its energy does not change when scattering on electrons.

### Problem 4

problem id:

Estimate the angular scale of the CMB anisotropy due to the Silk effect.