CMB Spectral Distortions from the Scattering of Temperature Anisotropies

TL;DR

This paper develops a non-perturbative formalism to compute spectral distortions in the CMB caused by scattering of temperature anisotropies, revealing effects significant at high redshifts and in non-standard cosmologies.

Contribution

It introduces a Lorentz invariant, non-perturbative formalism for calculating CMB spectral distortions from temperature anisotropies, applicable to inhomogeneous cosmologies.

Findings

Spectral distortions are characterized by a parameter u ~ 3e-8.

At z > 5, these distortions dominate over other sources.

The effect could be larger in non-standard cosmological models.

Abstract

Thomson scattering of CMBR temperature anisotropies will cause the spectrum of the CMBR to differ from blackbody even when one resolves all anisotropies. A formalism for computing the anisotropic and inhomogeneous spectral distortions of intensity and polarization is derived in terms of Lorentz invariant central moments of the temperature distribution. The formalism is non-perturbative, requiring neither small anisotropies nor small metric or matter inhomogeneities; but it does assume cold electrons. The low order moments are not coupled to the higher order moments allowing one to truncate the equations without any loss of accuracy. This formalism is applied to a standard Lambda-CDM cosmology after reionization where the temperature anisotropies are dominated by the Doppler effect for the bulk motion of the gas with respect to the CMBR frame. The resultant spectral distortion is parameterized by u ~ 3e-8, where in this case u is observationally degenerate with the Sunyaev-Zel'dovich (SZ) y parameter. In comparison the expected thermal SZ y-distortion from the hot IGM is expected to be >30 times larger. However at z >5 the effect described here would have been the dominant source of spectral distortions. The effect could be much larger in non-standard cosmologies.