Thermodynamics of Quasi-Topological Cosmology

TL;DR

This paper explores the thermodynamical properties of the apparent horizon in quasi-topological gravity, deriving Friedmann equations via two methods and confirming the deep link between thermodynamics and gravitational dynamics.

Contribution

It derives the Friedmann equations in quasi-topological gravity using variational and thermodynamic approaches, establishing their equivalence and analyzing the generalized second law of thermodynamics.

Findings

Both approaches yield the same Friedmann equation.

The generalized second law holds at late times under local equilibrium.

Confirms the connection between thermodynamics and gravity in quasi-topological cosmology.

Abstract

In this paper, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, $r_{+}$, with the apparent horizon radius, $\tilde{r}_{A}$, we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which show the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology.