Greens function of the cosmological thermalization problem II: effect of photon injection and constraints

The energy spectrum of the cosmic microwave background (CMB) provides a powerful tool for constraining standard and non-standard physics in the primordial Universe. Previous studies mainly highlight spectral distortions (mu-, y- and r-type) created by episodes of early energy release; however, several processes also lead to copious photon production, which requires a different treatment. Here, we carry out a first detailed study for the evolution of distortions caused by photon injection at different energies in the CMB bands. We provide detailed analytical and numerical calculations illustrating the rich phenomenology of the associated distortion signals. We show that photon injection at very high and very low frequencies creates distortions that are similar to those from pure energy release. In the mu-era (z>3x10^5), a positive or negative chemical potential can be formed, depending on the balance between added photon energy and number. At lower redshifts (z<3x10^5), partial information about the photon injection process (i.e., injection time and energy) can still be recovered, with the distortion being found in a partially comptonized state. We briefly discuss current and future constraints on scenarios with photon production. We also argue that more detailed calculations for different scenarios with photon injection may be required to assess in which regimes these can be distinguished from pure energy release processes.

Probing the scale dependence of non-Gaussianity with spectral distortions of the cosmic microwave background

Many inflation models predict that primordial density perturbations have a nonzero three-point correlation function, or bispectrum in Fourier space. Of the several possibilities for this bispectrum, the most commmon is the local-model bispectrum, which can be described as a spatial modulation of the small-scale (large-wavenumber) power spectrum by long-wavelength density fluctuations. While the local model predicts this spatial modulation to be scale-independent, many variants have some scale-dependence. Here we note that this scale dependence can be probed with measurements of frequency-spectrum distortions in the cosmic microwave background (CMB), in particular highlighting Compton-$y$ distortions. Dissipation of primordial perturbations with wavenumbers $50,{rm Mpc}^{-1} lesssim k lesssim 10^4,{rm Mpc}^{-1}$ give rise to chemical-potential ($mu$) distortions, while those with wavenumbers $1,{rm Mpc}^{-1} lesssim k lesssim 50,{rm Mpc}^{-1}$ give rise to Compton-$y$ distortions. With local-model non-Gaussianity, the distortions induced by this dissipation can be distinguished from those due to other sources via their cross-correlation with the CMB temperature $T$. We show that the relative strengths of the $mu T$ and $yT$ correlations thus probe the scale-dependence of non-Gaussianity and estimate the magnitude of possible signals relative to sensitivities of future experiments. We discuss the complementarity of these measurements with other probes of squeezed-limit non-Gaussianity.

Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe

Mixing of blackbodies with different temperatures creates a spectral distortion which, at lowest order, is a y-type distortion, indistinguishable from the thermal y-type distortion produced by the scattering of CMB photons by hot electrons residing in clusters of galaxies. This process occurs in the radiation-pressure dominated early Universe, when the primordial perturbations excite standing sound waves on entering the sound horizon. Photons from different phases of the sound waves, having different temperatures, diffuse through the electron-baryon plasma and mix together. This diffusion, with the length defined by Thomson scattering, dissipates sound waves and creates spectral distortions in the CMB. Of the total dissipated energy, 2/3 raises the average temperature of the blackbody part of spectrum, while 1/3 creates a distortion of y-type. It is well known that at redshifts 10^5< z< 2x10^6, comptonization rapidly transforms y-distortions into a Bose-Einstein spectrum. The chemical potential of the Bose-Einstein spectrum is again 1/3 the value we would get if all the dissipated energy was injected into a blackbody spectrum but no extra photons were added. We study the mixing of blackbody spectra, emphasizing the thermodynamic point of view, and identifying spectral distortions with entropy creation. This allows us to obtain the main results connected with the dissipation of sound waves in the early Universe in a very simple way. We also show that mixing of blackbodies in general, and dissipation of sound waves in particular, leads to creation of entropy.