Creation of the CMB spectrum: precise analytic solutions for the blackbody photosphere

Abstract

The blackbody spectrum of CMB was created in the blackbody photosphere at redshifts z>2x10^6. At these early 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>10^5 and result in a Bose-Einstein spectrum with a non-zero chemical potential ($\mu$). Precise evolution of the CMB spectrum around the critical redshift of z~2x10^6 is required in order to calculate the $\mu$-type spectral distortion and constrain the underlying new physics. 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 ~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 (~ 10^{-8}-10^{-10}).

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• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• Lines in the cosmic microwave background spectrum from the epoch of cosmological helium recombination
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Cited by in corpus (20)

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• Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe
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• CMB anisotropy and BBN constraints on pre-recombination decay of dark matter to visible particles
• CMB $\mu$ distortion from primordial gravitational waves
• The role of soft photon injection and heating in 21 cm cosmology
• Constraining CSL strength parameter $\lambda$ from standard cosmology and spectral distortions of CMBR
• Cosmological constraints from $\mu E$ cross-correlations
• Angular dependence of primordial trispectra and CMB spectral distortions
• New CMB spectral distortion constraints on decaying dark matter with full evolution of electromagnetic cascades before recombination
• CMB spectral distortions from continuous large energy release
• Anisotropic CMB distortions from non-Gaussian isocurvature perturbations
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating
• Spectral Distortions from Axion Monodromy Inflation
• Constraining broad photon spectrum injections from exotic and astrophysical sources
• EDGES of the dark forest: A new absorption window into the composite dark matter and large scale structure
• The non-thermal secondary CMB anisotropies from a cosmic distribution of radio galaxy lobes
• Spectral distortions in the decaying QCD dark matter scenario