Spectro-spatial evolution of the CMB III: transfer functions, power spectra and Fisher forecasts

TL;DR

This paper computes the transfer functions of spectral distortions in the CMB, linking early universe energy releases to observable signals, and forecasts how future experiments can improve constraints on these distortions.

Contribution

It provides the first detailed calculations of distortion transfer functions and demonstrates their use in constraining early energy releases with upcoming CMB experiments.

Findings

Power spectra levels are within current and future experimental constraints.

Future missions like LiteBIRD and PICO can significantly improve energy release limits.

Spectral distortion signals pose challenges for primordial non-Gaussianity measurements.

Abstract

In this paper, we provide the first computations for the distortion transfer functions of the cosmic microwave background (CMB) in the perturbed Universe, following up on paper I and II in this series. We illustrate the physical effects inherent to the solutions, discussing and demonstrating various limiting cases for the perturbed photon spectrum. We clarify the relationship between distortion transfer functions and the photon spectrum itself, providing the machinery that can then compute constrainable CMB signal power spectra including spectral distortions for single energy injection and decaying particle scenarios. Our results show that the $\mu \times T$ and $y\times T$ power spectra reach levels that can be constrained with current and future CMB experiments without violating existing constraints from COBE/FIRAS. The amplitude of the cross-correlation signal directly depends on the average distortion level, therefore establishing a novel fundamental link between the state of the primordial plasma from redshift $10^3 \lesssim z\lesssim 3\times 10^6$ and the frequency-dependent CMB sky. This provides a new method to constrain average early energy release using CMB imagers. As an example we derive constraints on single energy release and decaying particle scenarios. This shows that LiteBIRD may be able to improve the energy release limits of COBE/FIRAS by up to a factor of $\simeq 2.5$, while PICO could tighten the constraints by more than one order of magnitude. The signals considered here could furthermore provide a significant challenge to reaching cosmic variance-limited constraints on primordial non-Gaussianity from distortion anisotropy studies. Our work further highlights the immense potential for a synergistic spectroscopic approach to future CMB measurements and analyses.