The evolution of CMB spectral distortions in the early Universe

TL;DR

This work advances the quantitative study of CMB spectral distortions by introducing CosmoTherm, a code solving coupled photon Boltzmann and electron-temperature equations with improved double Compton, bremsstrahlung, and recombination treatments. It systematically assesses how different early-Universe energy-release channels—adiabatic cooling, acoustic-damping, annihilating and decaying particles, and quasi-instantaneous bursts—shape mu- and y-type distortions, plus low-frequency free-free features. Key findings show that acoustic damping can produce a detectable mu-like signal for near-fiducial spectral indices, while annihilating scenarios are more constrained by current anisotropy limits and model-dependent heating fractions; decaying relics yield strongly lifetime-dependent spectral shapes that could, in principle, be distinguished. The results underscore the importance of precise thermalization modeling and recombination physics for forecasting CMB spectral distortions with missions like Pixie, and they highlight the potential to extract additional constraints on the early thermal history of the Universe from the CMB energy spectrum.

Abstract

The energy spectrum of the cosmic microwave background (CMB) allows constraining episodes of energy release in the early Universe. In this paper we revisit and refine the computations of the cosmological thermalization problem. For this purpose a new code, called CosmoTherm, was developed that allows solving the coupled photon-electron Boltzmann equation in the expanding, isotropic Universe for small spectral distortion in the CMB. We explicitly compute the shape of the spectral distortions caused by energy release due to (i) annihilating dark matter; (ii) decaying relict particles; (iii) dissipation of acoustic waves; and (iv) quasi-instantaneous heating. We also demonstrate that (v) the continuous interaction of CMB photons with adiabatically cooling non-relativistic electrons and baryons causes a negative mu-type CMB spectral distortion of DI_nu/I_nu ~ 10^{-8} in the GHz spectral band. We solve the thermalization problem including improved approximations for the double Compton and Bremsstrahlung emissivities, as well as the latest treatment of the cosmological recombination process. At redshifts z <~ 10^3 the matter starts to cool significantly below the temperature of the CMB so that at very low frequencies free-free absorption alters the shape of primordial distortions significantly. In addition, the cooling electrons down-scatter CMB photons introducing a small late negative y-type distortion at high frequencies. We also discuss our results in the light of the recently proposed CMB experiment Pixie, for which CosmoTherm should allow detailed forecasting. Our current computations show that for energy injection because of (ii) and (iv) Pixie should allow to improve existing limits, while the CMB distortions caused by the other processes seem to remain unobservable with the currently proposed sensitivities and spectral bands of Pixie.

Figures (19)

• Figure 1: Effective double Compton correction factor $H_{\rm dc}(x)$. We compare the result from a full integration of a blackbody spectrum with the approximation given by Eq. \ref{['eq:H_DC_appr']}. For comparison also the approximation of Burigana1991 is shown. Close to the maximum of the CMB blackbody spectrum the differences are $\sim 20\%-40\%$.
• Figure 2: Evolution of the electron temperature for the standard thermal history. The electrons are always slightly cooler than ${T_{z}}$. For comparison we also show the evolution of the effective temperature of the photon field, $1-\rho^\ast=[{T_{z}}-{T_{\gamma}^\ast}]/{T_{z}}$, which also implies ${T_{\gamma}^\ast}<{T_{z}}$.
• Figure 3: CMB spectral distortion at $z=200$ caused by the continuous cooling from electrons. Neglecting the spectral distortion in the computation of the electron temperature leads to an underestimation of the final distortion at low frequencies. We also show a simple analytical fit according to Eq. \ref{['eq:n_x_app']} with parameters $\mu_\infty=-2.22 \times 10^{-9}$, $x_{\rm c}=1.5 \times 10^{-2}$, $\phi_{\rm f}-1=-8.0 \times 10^{-10}$, ${y_{\rm e}}=-4.3 \times 10^{-10}$ and ${y_{\rm ff}}=-4.17 \times 10^{-12}$.
• Figure 4: Evolution of the CMB spectral distortion caused by the continuous cooling from electrons. At low redshifts one can see the effect of electrons starting to cool significantly below the temperature of the photons, which leads to strong free-free absorption at very low frequencies.
• Figure 5: Evolution of the electron temperature for the standard thermal history with dissipation of energy by acoustic waves. As a result of the heating the electrons are always above ${T_{z}}$. For comparison we show the electron temperature obtained when neglecting this effect, for which in contrast one has $T_{\rm e}<{T_{z}}$ at all times.