A Logarithmic Correction in the Entropy Functional Formalism

TL;DR

This paper investigates how logarithmic corrections to entropy, common in quantum gravity, influence the entropy functional formalism and its ability to recover and constrain modified theories of gravity, especially F(R)-gravity.

Contribution

It demonstrates that logarithmic entropy corrections can be incorporated into the formalism, providing a way to derive and constrain modified gravity theories.

Findings

Logarithmic corrections can be integrated into the entropy functional formalism.

Such corrections lead to constraints on modified gravity theories.

Constraints match those from cosmological studies for F(R)-gravity.

Abstract

The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein-Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein-Hawking's entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an F(R)-gravity are the same as those obtained in the literature from cosmological considerations.