Statistical properties of CMB
Contents
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?
