Dynamics of non-minimally coupled perfect fluids

TL;DR

This paper develops a comprehensive framework for non-minimally coupled perfect fluids with conformal and disformal interactions, analyzing their equations of motion and implications for cosmology and astrophysics.

Contribution

It introduces a general formulation for non-minimally coupled perfect fluids, deriving modified Einstein and fluid equations, and explores their effects in cosmological and Newtonian contexts.

Findings

Euler equation is significantly modified by an extra curvature-related force.

Continuity equation remains unchanged, preserving conserved quantities.

Non-minimal coupling impacts cosmological perturbations and Newtonian limits.

Abstract

We present a general formulation of the theory for a non-minimally coupled perfect fluid in which both conformal and disformal couplings are present. We discuss how such non-minimal coupling is compatible with the assumptions of a perfect fluid and derive both the Einstein and the fluid equations for such model. We found that, while the Euler equation is significantly modified with the introduction of an extra force related to the local gradients of the curvature, the continuity equation is unaltered, thus allowing for the definition of conserved quantities along the fluid flow. As an application to cosmology and astrophysics we compute the effects of the non-minimal coupling on a Friedmann--Lema\^itre--Robertson--Walker metric at both background and linear perturbation level and on the Newtonian limit of our theory.