Statistical properties of CMB

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Problem 1: kinetic equation

Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe.

Problem 2: dipole component

The magnitude of the dipole component of anisotropy generated by the Solar system's motion relative to the relic radiation equals $\Delta T_d\simeq3.35mK$. Determine the velocity of the Solar system relative to the relic radiation.

Problem 3: annual variations

Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.

Problem 4: characteristic harmonic number

Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) as \[\Delta\theta={180^\circ}/{l_{max}}.\]

Problem 5: relativity

Does the measurement of velocity relative to the CMB mean violation of the relativity principle and an attempt to introduce an absolute reference frame?