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In terms of temperature and scale factor then $$T_0 = (1+z)^{-1} T_{rec},$$ where $T_{rec}$ is the recombination temperature and $T_0$ is the temperature of the CMB now. To put this interms of scale factor, we note that $a = (1+z)^{-1}$. So $$a_{rec} = \frac{T_0}{T_{rec}}$$ The universe is "matter-dominated" at the epoch of recombination and in this case $... 3 Yes. We can either look for the cosmic neutrino background or for gravitational waves associated with the big bang. Both of these probe the conditions considerably earlier than the the 380,000 years after the big-bang probed by the CMB. Neither of these are fanciful ideas - there are good theoretical reasons to expect both to exist, and in both cases there ... 1 From Quadrupole Types and Polarization Patterns Quadrupole anisotropies are associated with density, vorticity and gravitational wave fluctuations Their projection determines the polarization pattern and may be distinguished by symmetry properties The polarization probe more than just the density or temperature fluctuations at recombination. ... 1 The matter density scales as$a^{-3}$whilst the radiation density scales as$a^{-4}$. At the present epoch$\rho_{{\rm rad},0} \sim 6\times 10^{-5}$of the critical density, whereas$\rho_{{\rm mat},0} \sim 0.0486$of the critical density. At the epoch of recombination$z_{\rm rec} \sim 1100\$. This does indeed come from the Saha equation and is a ...

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Unpolarised light can be regarded as an equal mixture of perpendicular polarisations with random phases. The perpendicular polarisations cause perpendicular oscillations in an electron which then re-radiates in all directions except along the axis of an oscillation. The resultant scattered light is partially linearly polarised or completely linearly ...

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From facts about particle physics and thermodynamics, we get an equation of state, which describes the stress-energy tensor. The stress-energy determines the pressure and density, which show up in the Friedmann equations. You solve the Friedmann equations, and you get predictions for, e.g., when the CMB will have had a certain temperature.

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