CMB spectral distortions as solutions to the Boltzmann equations

Abstract

Distortions to the cosmic microwave background~(CMB) blackbody spectrum are calculated in the framework of cosmological perturbation theory. The second order Boltzmann equation is explicitly solved, with the spectral $y$ distortion and the frequency independent second order temperature perturbation. We also solve higher order Boltzmann equations systematically and find new type spectral distortions in the low energy limit of electrons. As an example, we concretely construct a solution to the cubic order Boltzmann equation and show that it can be characterized by three parameters: a cubic order temperature perturbation and two different types of cubic order spectral distortions. A new linear Sunyaev-Zel'dovich effect whose frequency dependence is different from the usual $y$ distortion is also discussed in the presence of the next-to-leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of the higher order cosmological perturbation theory. We also comment that generation of the spectral $\mu$ distortion cannot be explained in this framework even at second order.

35 pages, 1 figure, including major revisions, a lot of errors are corrected

References in corpus (18)

• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• Silk damping at a redshift of a billion: a new limit on small-scale adiabatic perturbations
• Beyond y and μ: the shape of the CMB spectral distortions in the intermediate epoch, 1.5x10^4 < z < 2x10^5
• Taking the Universe's Temperature with Spectral Distortions of the Cosmic Microwave Background
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Cosmological Perturbations at Second Order and Recombination Perturbed
• Probing the scale dependence of non-Gaussianity with spectral distortions of the cosmic microwave background
• Non-Gaussianities from Perturbing Recombination
• Spectral distortions from the dissipation of tensor perturbations
• CMB $\mu$ distortion from primordial gravitational waves
• Gauge invariant Boltzmann equation and the fluid limit
• Probing correlations of early magnetic fields using mu-distortion
• Cosmological constraints from $\mu E$ cross-correlations
• Geodesic "curve"-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing
• Anisotropic CMB distortions from non-Gaussian isocurvature perturbations
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating

Cited by in corpus (8)

• Spectral distortion anisotropies from single-field inflation
• Induced superhorizon tensor perturbations from anisotropic non-Gaussianity
• Exploring compensated isocurvature perturbations with CMB spectral distortion anisotropies
• Unified approach to secondary effects on the CMB B-mode polarization
• Statistical anisotropy in CMB spectral distortions
• Secondary isocurvature perturbations from acoustic reheating
• CMB spectroscopy at third-order in cosmological perturbations
• Cosmic microwave background spectral distortions from Rayleigh scattering at second order