Nonminimal coupling of perfect fluids to curvature

TL;DR

This paper investigates various forms of perfect fluid Lagrangians in modified gravity theories with nonminimal curvature coupling, revealing that different choices can lead to non-vanishing extra forces and affect classical equivalence.

Contribution

It demonstrates that the commonly used Lagrangian density ${ m{ extbf{L}}}_m = p$ is not unique and explores the implications of alternative forms on extra-force effects.

Findings

Different perfect fluid Lagrangians can induce non-zero extra forces.

The choice of Lagrangian density affects the classical equivalence of fluid descriptions.

Nonminimal coupling modifies the dynamics of perfect fluids in gravity theories.

Abstract

In this work, we consider different forms of relativistic perfect fluid Lagrangian densities, that yield the same gravitational field equations in General Relativity. A particularly intriguing example is the case with couplings of the form $[1+f_2(R)]{\cal L}_m$, where $R$ is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density ${\cal L}_m = p$, where $p$ is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for ${\cal L}_m$ do not imply the vanishing of the extra-force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.