Modified gravity from an entropy functional

TL;DR

This paper extends Padmanabhan's entropy functional approach to include a broader class of modified gravity theories, demonstrating its utility in deriving higher-order curvature corrections and calculating horizon entropy.

Contribution

The paper generalizes the entropy functional formalism to encompass more complex modified gravity theories beyond Gauss-Bonnet and Lanczos-Lovelock models.

Findings

Higher-order curvature corrections naturally emerge from the extended formalism.

The formalism successfully computes horizon entropy in a second-order modified gravity theory.

Results align with existing literature on modified gravity entropy calculations.

Abstract

We extend Padmanabhan's entropy functional formalism to show that, in addition to the Gauss-Bonnet or the entire series of Lanczos-Lovelock Lagrangians already obtained, more general higher-order corrections to General Relativity, i.e., the so-called modified gravity theories, also emerge naturally from this formalism. This extension shows that the formalism constitutes a valuable tool to investigate, at each order in the curvature, the possible structure the higher-order modified gravity theories might have. As an application, the extended formalism is used to evaluate the horizon entropy in a modified gravity theory of the second-order in the curvature. Our findings are in agreement with previous results from the literature.