The evolution of CMB spectral distortions in the early Universe

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.Comment: 22 pages, 19 figures, 1 table, accepted by MNRA

CMB at 2x2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release

Silk damping of primordial small-scale perturbations in the photon-baryon fluid due to diffusion of photons inevitably creates spectral distortions in the CMB. With the proposed CMB experiment PIXIE it might become possible to measure these distortions and thereby constrain the primordial power spectrum at comoving wavenumbers 50 Mpc^{-1} < k < 10^4 Mpc^{-1}. Since primordial fluctuations in the CMB on these scales are completely erased by Silk damping, these distortions may provide the only way to shed light on otherwise unobservable aspects of inflationary physics. A consistent treatment of the primordial dissipation problem requires going to second order in perturbation theory, while thermalization of these distortions necessitates consideration of second order in Compton scattering energy transfer. Here we give a full 2x2 treatment for the creation and evolution of spectral distortions due to the acoustic dissipation process, consistently including the effect of polarization and photon mixing in the free streaming regime. We show that 1/3 of the total energy (9/4 larger than previous estimates) stored in small-scale temperature perturbations imprints observable spectral distortions, while the remaining 2/3 only raises the average CMB temperature, an effect that is unobservable. At high redshift dissipation is mainly mediated through the quadrupole anisotropies, while after recombination peculiar motions are most important. During recombination the damping of the higher multipoles is also significant. We compute the average distortion for several examples using CosmoTherm, analyzing their dependence on parameters of the primordial power spectrum. For one of the best fit WMAP7 cosmologies, with n_S=1.027 and n_run=-0.034, the cooling of baryonic matter practically compensates the heating from acoustic dissipation in the mu-era. (abridged)Comment: 40 pages, 17 figures, accepted by MNRA

Pre-recombinational energy release and narrow features in the CMB spectrum

Energy release in the early Universe (z<~ 2x10^6) should lead to some broad spectral distortion of the cosmic microwave background (CMB) radiation field, which can be characterized as y-type distortion when the injection process started at redshifts z<~ 5x10^4. Here we demonstrate that if energy was released before the beginning of cosmological hydrogen recombination (z~1400), closed loops of bound-bound and free-bound transitions in HI and HeII lead to the appearance of (i) characteristic multiple narrow spectral features at dm and cm wavelengths, and (ii) a prominent sub-millimeter feature consisting of absorption and emission parts in the far Wien tail of CMB spectrum. The additional spectral features are generated in the pre-recombinational epoch of HI (z>~1800) and HeII (z>~7000), and therefore differ from those arising due to normal cosmological recombination in the undisturbed CMB blackbody radiation field. We present the results of numerical computations including 25 atomic shells for both HI and HeII, and discuss the contributions of several individual transitions in detail. As examples, we consider the case of instantaneous energy release (e.g. due to phase transitions) and exponential energy release because of long-lived decaying particles. Our computations show that due to possible pre-recombinational atomic transitions the variability of the CMB spectral distortion increases when comparing with the distortions arising in the normal recombination epoch. The existence of these narrow spectral features would open an unique way to separate y-distortions due to pre-recombinational ($1400<~ z <~5x10^4) energy release from those arising in the post-recombinational era at redshifts z<~800. (abridged)Comment: 17 pages, 12 Figures, 1 Table, submitted to A&

Rethinking CMB foregrounds: systematic extension of foreground parameterizations

Future high-sensitivity measurements of the cosmic microwave background (CMB) anisotropies and energy spectrum will be limited by our understanding and modeling of foregrounds. Not only does more information need to be gathered and combined, but also novel approaches for the modeling of foregrounds, commensurate with the vast improvements in sensitivity, have to be explored. Here, we study the inevitable effects of spatial averaging on the spectral shapes of typical foreground components, introducing a moment approach, which naturally extends the list of foreground parameters that have to be determined through measurements or constrained by theoretical models. Foregrounds are thought of as a superposition of individual emitting volume elements along the line of sight and across the sky, which then are observed through an instrumental beam. The beam and line of sight averages are inevitable. Instead of assuming a specific model for the distributions of physical parameters, our method identifies natural new spectral shapes for each foreground component that can be used to extract parameter moments (e.g., mean, dispersion, cross-terms, etc.). The method is illustrated for the superposition of power-laws, free-free spectra, gray-body and modified blackbody spectra, but can be applied to more complicated fundamental spectral energy distributions. Here, we focus on intensity signals but the method can be extended to the case of polarized emission. The averaging process automatically produces scale-dependent spectral shapes and the moment method can be used to propagate the required information across scales in power spectrum estimates. The approach is not limited to applications to CMB foregrounds but could also be useful for the modeling of X-ray emission in clusters of galaxies.Comment: 19 pages, 8 figures, accepted by MNRAS, minor revision