Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem

TL;DR

This paper develops a generally covariant scalar field model incorporating high-frequency dispersion, analyzing its effects on cosmology and the horizon problem, and finds superluminal dispersion can address horizon issues under certain conditions.

Contribution

It introduces a covariant framework for high-frequency dispersion in scalar fields, allowing analysis of its cosmological implications and potential to solve the horizon problem.

Findings

High-temperature equation of state is slightly altered but not enough to affect big bang cosmology.

Superluminal dispersion can solve the horizon problem through superluminal equilibration.

Artificially steep dispersion relations are needed to address horizon issues outside the Planck regime.

Abstract

Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally covariant metric theory of gravity provided the locally preferred frame is dynamical. We evaluate the resulting energy-momentum tensor and compute its expectation value for a quantum field in a thermal state. The equation of state differs at high temperatures from the usual one, but not by enough to impact the problems of a hot big bang cosmology. We show that a superluminal dispersion relation can solve the horizon problem via superluminal equilibration, however it cannot do so while remaining outside the Planck regime unless the dispersion relation is artificially chosen to have a rather steep dependence on wavevector.