Corrected Entropy of Friedmann-Robertson-Walker Universe in Tunneling Method

TL;DR

This paper derives a universal corrected entropy formula for the apparent horizon in FRW universes across various gravity theories using tunneling formalism beyond semiclassical approximation, confirming its independence from specific theories or dimensions.

Contribution

It introduces a generalized corrected entropy expression for FRW universe horizons applicable to multiple gravity theories, extending tunneling method beyond semiclassical approximation.

Findings

Corrected entropy formula is universal across gravity theories.

The corrected entropy is a state function for the FRW universe.

The formula applies to black holes as well.

Abstract

In this paper, we study the thermodynamic quantities of Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism beyond semiclassical approximation developed by \emph{Banerjee} and \emph{Majhi}\cite{beyond0}. For this we first calculate the corrected Hawking-like temperature on apparent horizon by considering both scalar particle and fermion tunneling. With this corrected Hawking-like temperature, the explicit expressions of the corrected entropy of apparent horizon for various gravity theories including Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, $f(R)$ gravity and scalar-tensor gravity, are computed. Our results show that the corrected entropy formula for different gravity theories can be written into a general expression (\ref{entropy-final}) of a same form. It is also shown that this expression is also valid for black holes. This might imply that the expression for the corrected entropy derived from tunneling method is independent of gravity theory, spacetime and dimension of the spacetime. Moreover, it is concluded that the basic thermodynamical property that the corrected entropy on apparent horizon is a state function is satisfied by the FRW universe.