Dark energy in thermal equilibrium with the cosmological horizon?

TL;DR

This paper investigates the conditions under which dark energy and other cosmological fluids can be in thermal equilibrium with the horizon, revealing constraints on energy transfer rates and potential violations of energy conservation.

Contribution

It derives specific restrictions on energy transfer rates for dark energy models in thermal equilibrium with the horizon, considering holographic and constant EoS dark energy.

Findings

Unique energy transfer term for each dark energy type at fixed horizon radius

Thermal equilibrium conditions impose constraints on interaction terms

Energy conservation may be violated when multiple fluids are in equilibrium with the horizon

Abstract

According to a generalization of black hole thermodynamics to a cosmological framework, it is possible to define a temperature for the cosmological horizon. The hypothesis of thermal equilibrium between the dark energy and the horizon has been considered by many authors. We find the restrictions imposed by this hypothesis on the energy transfer rate ($Q_i$) between the cosmological fluids, assuming that the temperature of the horizon have the form $T=b/2\pi R$, where $R$ is the radius of the horizon. We more specifically consider two types of dark energy: holographic dark energy (HDE) and dark energy with a constant EoS parameter ($w$DE). In each case, we show that for a given radius $R$, there is an unique term $Q_{de}$ that is consistent with thermal equilibrium. We also consider the situation where, in addition to dark energy, other fluids (cold matter, radiation) are in thermal equilibrium with the horizon. We find that the interaction terms required for this will generally violate energy conservation ($\sum_i Q_i=0$).