Time Evolution of CMB

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Problem 1

Show that in the expanding Universe the quantity $aT$ is an approximate invariant.


Problem 1

Show that the electromagnetic radiation frequency decreases with expansion of Universe as $\omega(t)\propto a(t)^{-1}$.


Problem 1

Show that if the radiation spectrum was equilibrium at some initial moment, then it will remain equilibrium during the following expansion.


Problem 1

Find the CMB temperature one second after the Big Bang.


Problem 1

Show that creation of the relic radiation (the photon decoupling) took place in the matter-dominated epoch.


Problem 1

What color had the sky at the recombination epoch?


Problem 1

When the night sky started to look black?


Problem 1

Estimate the moment of time when the CMB energy density was comparable to that in the microwave oven.


Problem 1

Estimate the moment of time when the CMB wavelength will be comparable to that in the microwave oven, which is $\lambda=12.6\ cm$.


Problem 1

When the relic radiation obtained formal right to be called CMB? And for what period of time?


Problem 1

Calculate the presently observed density of photons for the CMB and express it in Planck units.


Problem 1

Find the ratio of CMB photons' energy density to that of the neutrino background.


Problem 1

Determine the average energy of a CMB photon at present time.


Problem 1

Why, when calculating the energy density of electromagnetic radiation in the Universe, we can restrict ourself to the CMB photons?


Problem 1

The relation $\rho_\gamma\propto a^{-4}$ assumes conservation of photon's number. Strictly speaking, this assumption is inaccurate. The Sun, for example, emits of the order of $10^{45}$ photons per second. Estimate the accuracy of this assumption regarding the photon's number conservation.


Problem 1

Can hydrogen burning in the thermonuclear reactions provide the observed energy density of the relic radiation?


Problem 1

Find the ratio of relic radiation energy density in the epoch of last scattering to the present one.


Problem 1

Find the ratio of average number densities of photons to baryons in the Universe.


Problem 1

Explain qualitatively why the temperature of photons at the surface of last scattering (0.3 eV) is considerably less than the ionization energy of the hydrogen atom (13.6 eV).


Problem 1

Estimate the moment of the beginning of recombination-transition from ionized plasma to gas of neutral atoms.


Problem 1

Determine the moment of time when the mean free path of photons became of the same order as the current observable size of Universe).


Problem 1

How will the results of problem and problem change if one takes into account the possibility of creation of neutral hydrogen in excited states?


Problem 1

Why is the cosmic neutrino background (CNB) temperature at present lower than the one for CMB?