The generalized second law of thermodynamics in Horava-Lifshitz cosmology

TL;DR

This paper examines whether the generalized second law of thermodynamics holds in Horava-Lifshitz cosmology, finding it generally valid under certain conditions and highlighting potential issues with the gravity theory.

Contribution

It analyzes the validity of the generalized second law in Horava-Lifshitz gravity, considering different scenarios and revealing limitations of the effective approach.

Findings

GSL is valid for flat and closed geometries under detailed balance.

GSL is conditionally valid for open universes and beyond detailed balance.

The effective approach can lead to misleading conclusions.

Abstract

We investigate the validity of the generalized second law of thermodynamics in a universe governed by Horava-Lifshitz gravity. Under the equilibrium assumption, that is in the late-time cosmological regime, we calculate separately the entropy time-variation for the matter fluid and, using the modified entropy relation, that of the apparent horizon itself. We find that under detailed balance the generalized second law is generally valid for flat and closed geometry and it is conditionally valid for an open universe, while beyond detailed balance it is only conditionally valid for all curvatures. Furthermore, we also follow the effective approach showing that it can lead to misleading results. The non-complete validity of the generalized second law could either provide a suggestion for its different application, or act as an additional problematic feature of Horava-Lifshitz gravity.