Thermodynamics of spacetime and unimodular gravity

TL;DR

This review explores how thermodynamic principles lead to unimodular gravity, highlighting its unique features like the cosmological constant and energy-momentum conservation, and contrasting it with fully diffeomorphism invariant theories.

Contribution

It demonstrates that thermodynamic derivations favor unimodular gravity over fully diffeomorphism invariant theories, even in modified gravity contexts.

Findings

Unimodular gravity naturally emerges from thermodynamic arguments.

The cosmological constant is treated as an integration constant.

Unimodular dynamics differ from fully diffeomorphism invariant theories.

Abstract

In this review we discuss emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation.