Fifty shades of grayness: parametrizations of spectral distortions and applications in cosmology

TL;DR

This paper introduces new parametrization methods for spectral distortions in cosmology, enabling efficient and flexible modeling of deviations from thermal spectra in neutrinos and photons, with applications to constraining nonstandard relic distortions.

Contribution

It extends existing approaches by developing a polynomial-based parametrization of spectral distortions, offering computational advantages and broad applicability in cosmological studies.

Findings

Efficient description of standard spectral distortions in neutrinos and photons.

Model-independent constraints on nonstandard relic distortions.

Demonstration of the polynomial parametrization's flexibility and computational ease.

Abstract

Thermal distribution functions can only be of the Fermi-Dirac or Bose-Einstein types, whereas distorted spectra encompass any possible deviations from these shapes. It is fruitful to devise parametrizations of these distortions with only a few parameters which depend on the physical system considered. A method proposed by Stebbins consists in describing a distorted spectrum as a sum of thermalized spectra with a distribution of temperatures, the moments of which are the parameters of interest. After revisiting and extending this approach by working at the level of the number density distribution instead of the standard spectrum, we build another method which consists in describing the distorted spectrum by a polynomial modulating a reference thermalized spectrum. The distortion parameters are then the coefficients of a decomposition on a suitable orthonormal polynomial basis. We advocate that the latter is computationally easier and allows to describe a wide range of distortions. With this formalism, we efficiently describe the standard distortions of the cosmological backgrounds of neutrinos and photons, and we obtain model-independent constraints on nonstandard distortions of these cosmological relics.