Higher-derivative Lorentz-breaking dispersion relations: a thermal description

A A Araújo Filho,A Yu Petrov

doi:10.1140/epjc/s10052-021-09639-y

Abstract

This paper is devoted to study the thermal aspects of a photon gas within the context of Planck-scale-modified dispersion relations. We study the spectrum of radiation and the correction to the Stefan–Boltzmann law in different cases when the Lorentz symmetry is no longer preserved. Explicitly, we examine two models within the context of CPT-even and CPT-odd sectors respectively. To do so, three distinct scenarios of the Universe are considered: the Cosmic Microwave Background (CMB), the electroweak epoch, and the inflationary era. Moreover, the equations of state in these cases turn out to display a dependence on Lorentz-breaking parameters. Finally, we also provide for both theories the analyses of the Helmholtz free energy, the mean energy, the entropy and the heat capacity.

Highlights

The Lorentz invariance is a well-established symmetry of the nature, its possible violation is assumed within many contexts [1,2,3]
We considered the thermodynamical aspects of two higherderivative Lorentz-breaking theories, namely, CPT-even and CPT-odd ones
We focused on the dispersion relations rather than the specific form of the Lagrangians

Summary

Introduction

The Lorentz invariance is a well-established symmetry of the nature, its possible violation is assumed within many contexts [1,2,3]. Studies on the thermodynamics of LV extensions of various field theory models could provide additional information about initial stages of expansion of the Universe, whose size at these stages was compatible with characteristic scales of Lorentz symmetry breaking [9]. We note that the dispersion relations that we consider in the present manuscript might possibly be used to describe some quantum gravity effects (see discussions in [27]), or, at least, they can probably arise in some LV extensions of QED. Our results involving thermal radiation may be confronted with experimental data as soon as they are available In this sense, our study might help in the investigation of any trace of the Lorentz violation within cosmological scenarios concerning thermal radiation as the starting point

Thermodynamical aspects of CPT-even higher-derivative LV theory

Thermodynamical aspects of CPT-odd higher-derivative LV theory

Conclusion