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}).

References in corpus (30)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Supersymmetric Dark Matter
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Relic neutrino decoupling including flavour oscillations
• The Primordial Inflation Explorer (PIXIE): A Nulling Polarimeter for Cosmic Microwave Background Observations
• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
• Particle decays during the cosmic dark ages
• The evolution of CMB spectral distortions in the early Universe
• Detecting Dark Matter Annihilation with CMB Polarization : Signatures and Experimental Prospects
• Observations of Milky Way Dwarf Spheroidal galaxies with the Fermi-LAT detector and constraints on Dark Matter models
• Nuclear Reaction Network for Primordial Nucleosynthesis: a detailed analysis of rates, uncertainties and light nuclei yields
• CMB at 2x2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release
• Constraints on Cosmological Dark Matter Annihilation from the Fermi-LAT Isotropic Diffuse Gamma-Ray Measurement
• Power Spectrum Constraints from Spectral Distortions in the Cosmic Microwave Background
• The NACRE Thermonuclear Reaction Compilation and Big Bang Nucleosynthesis
• Neutralinos, Big Bang Nucleosynthesis and 6Li in Low-Metallicity Stars
• Could the Cosmological Recombination Spectrum Help Us Understand Annihilating Dark Matter?
• Lines in the cosmic microwave background spectrum from the epoch of cosmological helium recombination
• Does Bose-Einstein condensation of CMB photons cancel μ distortions created by dissipation of sound waves in the early Universe?
• Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments
• Implications of the Fermi-LAT diffuse gamma-ray measurements on annihilating or decaying Dark Matter
• Relativistic Thermal Bremsstrahlung Gaunt Factor for the Intracluster Plasma. II. Analytic Fitting Formulae
• Time of primordial Be-7 conversion into Li-7, energy release and doublet of narrow cosmological neutrino lines
• A numerical code for the solution of the Kompaneets equation in cosmological context
• An Enhanced Cosmological Li6 Abundance as a Potential Signature of Residual Dark Matter Annihilations

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• Distinguishing different scenarios of early energy release with spectral distortions of the cosmic microwave background
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• CMB spectral distortions from small-scale isocurvature fluctuations
• CMB and BBN constraints on evaporating primordial black holes revisited
• The synergy between CMB spectral distortions and anisotropies
• Green's function of the cosmological thermalization problem II: effect of photon injection and constraints
• The blackness of the cosmic microwave background spectrum as a probe of the distance-duality relation
• Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe
• Observational Constraints on Gauge Field Production in Axion Inflation
• Unavoidable CMB spectral features and blackbody photosphere of our Universe
• A Hydrodynamical Approach to CMB mu-distortions
• Forecasts for CMB μ- and i-type spectral distortion constraints on the primordial power spectrum on scales 8 < k < 10^4 Mpc^-1 with the future Pixie-like experiments
• Thermalization of large energy release in the early Universe
• $\mu$-Distortions or Running: A Guaranteed Discovery from CMB Spectrometry
• Refined approximations for the distortion visibility function and mu-type spectral distortions
• CMB anisotropy and BBN constraints on pre-recombination decay of dark matter to visible particles
• Non-thermal WIMPs as "Dark Radiation" in Light of ATACAMA, SPT, WMAP9 and Planck
• CMB $\mu$ distortion from primordial gravitational waves
• Polarized anisotropic spectral distortions of the CMB: Galactic and extragalactic constraints on photon-axion conversion
• Constraints on hidden photons from current and future observations of CMB spectral distortions
• 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
• Primordial trispectra and CMB spectral distortions
• CMB distortion anisotropies due to the decay of primordial magnetic fields
• A new probe of Axion-Like Particles: CMB polarization distortions due to cluster magnetic fields
• 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
• Measuring primordial anisotropic correlators with CMB spectral distortions
• Cosmic Microwave Background Constraints on Dark Matter Models of the Galactic Center 511 keV Signal
• Limits on the fluctuating part of $y$-type distortion monopole from Planck and SPT results
• Constraints on non-resonant photon-axion conversion from the Planck satellite data
• Radiation in equilibrium with plasma and plasma effects on cosmic microwave background
• The effects of the small-scale behaviour of dark matter power spectrum on CMB spectral distortion
• CMB spectral distortions from continuous large energy release
• Anisotropic CMB distortions from non-Gaussian isocurvature perturbations
• FSD: Frequency Space Differential measurement of CMB spectral distortions
• Cosmological Constraints on Unstable Particles: Numerical Bounds and Analytic Approximations
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating
• CMB Spectral Distortions from Cooling Macroscopic Dark Matter
• Constraints on $N_{\mathrm{eff}}$ of high energy non-thermal neutrino injections upto $z\sim 10^8$ from CMB spectral distortions and abundance of light elements
• Spectral Distortions from Axion Monodromy Inflation
• Testing kinetically coupled inflation models with CMB distortions
• Energy injection in pre-recombination era and EDGES detection
• Constraining broad photon spectrum injections from exotic and astrophysical sources
• Primordial nucleosynthesis constraints on high-z energy releases
• 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