The $a$-theorem and temperature of the CMB temperature in cosmology

TL;DR

This paper explores how the initial conditions of the universe imply a thermal component in the CMB spectrum, influenced by the trace anomaly and the -theorem, potentially affecting cosmological observations.

Contribution

It introduces a mechanism linking the -theorem to the thermal properties of the CMB, providing a novel way to understand the primordial spectrum's tilt.

Findings

Thermal contribution to the CMB red tilt is linked to the trace anomaly.

The effect is too small for low spins but can be amplified via the -theorem.

The -coefficient influences the magnitude of the thermal effect.

Abstract

Initial conditions in cosmology in the form of the microcanonical density matrix of the Universe predict a thermal nature of the primordial CMB power spectrum with a nonzero temperature of the resulting relict temperature distribution. This effect generates a thermal contribution to the red tilt of this spectrum, additional to its vacuum component. In the cosmological model with a large number of free fields conformally coupled to gravity the magnitude of this effect is determined by the Gauss-Bonnet coefficient $\mbox{\boldmath$a$}$ of the trace anomaly. For low spins it is too small to be presently observable, but it can be amplified by the mechanism of the $\mbox{\boldmath$a$}$-theorem applied to the renormalization group flow which interpolates between the ultraviolet and infrared domains associated respectively with early and late stages of cosmological evolution.