Cosmic Energy Density: Particles, Fields and the Vacuum

TL;DR

This paper investigates the evolution of energy density of a quantized scalar field in the universe, comparing particle production and classical field approximations, with implications for dark energy and dark matter models.

Contribution

It provides a detailed analysis of the conditions under which classical and quantum approximations accurately predict cosmic energy density, using Pauli-Villars regularization.

Findings

Classical and quantum approximations can sometimes misestimate energy density.

The in vacuum state influences subsequent energy density evolution.

Certain transition models avoid common issues in the literature.

Abstract

We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the {\it in} vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.