How hot are expanding universes ?

TL;DR

This paper derives a comprehensive formula for the temperature experienced by moving observers in expanding universes, linking quantum field theory, thermodynamics, and cosmology, and clarifies conditions for thermality in such spacetimes.

Contribution

It presents the most general expression for observer temperature in dynamic Hubble universes, extending previous results limited to constant accelerations and Hubble parameters.

Findings

Derived a universal temperature formula for moving observers in expanding universes.

Identified conditions under which Friedman universes exhibit thermal vacuum states.

Clarified the distinction between constant temperature and true thermality.

Abstract

A way to address the conundrum of Quantum Gravity is to illustrate the potentially fundamental interplay between quantum field theory, curved space-times physics and thermodynamics. So far, when studying moving quantum systems in the vacuum, the only known perfectly thermal temperatures are those obtained for constant (or null) accelerations $A$ in constant (or null) Hubble parameters $H$ space-times. In this Letter, restricting ourselves to conformally coupled scalar fields, we present the most comprehensive expression for the temperature undergone by a moving observer in the vacuum, valid for any time-dependent linear accelerations and Hubble parameters: $T=\sqrt{A^2 + H^2 + 2 \dot H\dot t}/{2\pi}$ where $\dot t=\d t/\d\t$ is the motion's Lorentz factor. The inequivalence between a constant $T$ and actual thermality is explained. As a byproduct, all the Friedman universes for which observers at rest feel the vacuum as a thermal bath are listed.