Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2012-03-12
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
Submitted
Scientific paper
The blackbody spectrum of CMB was created behind the blackbody surface at redshifts $z\gtrsim 2\times 10^6$. At earlier times, the Universe was dense and hot enough that complete thermal equilibrium between baryonic matter (electrons and ions) and photons could be established. Any perturbation away from the blackbody spectrum was suppressed exponentially. New physics, for example annihilation and decay of dark matter, can add energy and photons to CMB at redshifts $z\gtrsim 10^5$ and result in a non-zero chemical potential ($\mu$) of CMB. Precise evolution of the CMB spectrum around the critical redshift of $z\gtrsim 2\times 10^6$ is required in order to calculate the $\mu$-type spectral distortion. Although numerical calculation of important processes involved (double Compton process, comptonization and bremsstrahlung) is not difficult, analytic solutions are much faster and easier to calculate and provide valuable physical insights. We provide precise (better than 1%) analytic solutions for the decay of $\mu$, created at an earlier epoch, including all three processes, double Compton, Compton scattering on thermal electrons and bremsstrahlung in the limit of small distortions. This is a significant improvement over the existing solutions with accuracy $\sim 10%$ or worse. We also give a census of important sources of energy injection into CMB in standard cosmology. In particular, calculations of distortions from electron-positron annihilation and primordial nucleosynthesis illustrate in a dramatic way the strength of the equilibrium restoring processes in the early Universe. Finally, we point out the triple degeneracy in standard cosmology, i.e., the $\mu$ and $y$ distortions from adiabatic cooling of baryons and electrons, Silk damping and annihilation of thermally produced WIMP dark matter are of similar order of magnitude ($\sim 10^{-8}-10^{-10}$).
Khatri Rishi
Sunyaev Rashid A.
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