Improved frequency hierarchy treatment for anisotropic spectral distortions

TL;DR

This paper enhances the frequency hierarchy method for analyzing anisotropic spectral distortions in the CMB, incorporating additional physical effects for more accurate modeling of early Universe signals.

Contribution

It introduces a modified evolution equation formalism that includes stimulated scattering, kinematic corrections, and photon sources, improving the accuracy of spectral distortion predictions.

Findings

Previous results remain largely unchanged with the new formalism.

The improved method enables modeling of spectral distortions from photon-dark photon and photon-axion conversions.

Illustrates how temperature-redshift variations affect spectral anisotropies.

Abstract

Spectral distortion anisotropies of the cosmic microwave background (CMB) provide a new probe of the early Universe that can be accessed using traditional CMB imaging techniques. It is possible to compute the creation and evolution of anisotropic signals for various scenarios using the frequency hierarchy method recently developed for CosmoTherm. However, the current treatment is not perfect and some approximations had to be made. Here, we carefully construct a modified form for the evolution equations that has the full equilibrium solutions built into the formulation. We improve the formalism to account for i) additional stimulated scattering effects, ii) kinematic corrections to the thermalization terms, iii) corrections to the standard perturbation variables and iv) direct photon sources. These effect could not be captured with the original formulation of the frequency hierarchy method but are indeed important for cleanly separating real distortions from temperature signals. However, we show that previous results are not altered significantly when compared to the improved formulation presented here. As a new worked example, which could indeed not be treated before, we also illustrate how possible changes in the temperature-redshift relation would create spectral distortion anisotropies in the pre-recombination era. The theoretical methods presented here are also an important step towards being able to consistently predict the CMB spectral distortion anisotropies in photon-dark photon and photon-axion conversion scenarios.