The Lagrangian description of perfect fluids and modified gravity with an extra force

TL;DR

This paper examines how different Lagrangian formulations of perfect fluids affect predictions in modified gravity theories with nonminimal matter coupling, highlighting the importance of the correct Lagrangian choice.

Contribution

It clarifies the impact of Lagrangian choice on the behavior of perfect fluids in nonminimally coupled gravity theories, emphasizing the distinction from minimal coupling cases.

Findings

Different Lagrangians lead to distinct predictions in nonminimal coupling scenarios.

Minimal coupling Lagrangians are only equivalent to pressure versus minus energy density formulations.

Nonminimal coupling breaks the equivalence between different fluid Lagrangian descriptions.

Abstract

We revisit the issue of the correct Lagrangian description of a perfect fluid (pressure versus minus energy density) in relation with modified gravity theories in which galactic luminous matter couples nonminimally to the Ricci scalar. These Lagrangians are only equivalent when the fluid couples minimally to gravity and not otherwise; in the presence of nonminimal coupling they give rise to two distinct theories with different predictions.