The correspondence of generalised entropic cosmology theory with $F(T)$ and $F(Q)$ modified gravity and gravitational waves

TL;DR

This paper explores the connection between entropic cosmology and modified gravity theories, showing how $F(T)$ and $F(Q)$ gravities relate to entropic gravity and analyzing their effects on gravitational waves.

Contribution

It establishes a correspondence between entropic cosmology and $F(T)$, $F(Q)$ gravity theories, and examines their implications for gravitational wave behavior.

Findings

$F(T)$ and $F(Q)$ gravity correspond to entropic gravity.

Gravitational wave equations are similar to Einstein's, with modified coupling.

Tsallis entropic cosmology can suppress or enhance gravitational wave emission.

Abstract

We investigate the correspondence between modified gravity theories and general entropic cosmology theory. Such a theory is proposed by an analogy with Jacobson's work, where the Einstein equation was derived from the Bekenstein-Hawking entropy. We compare FLRW equations obtained in entropic gravity with those in modified gravity theories. It is found the correspondence of $F(T)$ and $F(Q)$ gravities and general entropic gravity. We regard the $F(T)$ and $F(Q)$ gravity theories as effective local theories corresponding to the entropic gravity theories and we investigate the gravitational waves. The obtained equation of the gravitational wave is identical to that in Einstein's gravity except that the gravitational coupling is modified by the functional form of the functions $F(T)$ and $F(Q)$. It is interesting that in the case of the Tsallis entropic cosmology, the gravitational coupling becomes small or large, which may suppress or enhance the emission of the gravitational wave.