Density perturbations in nonminimally coupled gravity: symptoms of Lagrangian density ambiguity

TL;DR

This paper investigates how different choices of matter Lagrangian affect density perturbations in nonminimally coupled gravity, revealing potential singularities and constraints, and proposing solutions for physically consistent models.

Contribution

It analyzes the impact of matter Lagrangian choices on density perturbations in nonminimally coupled gravity, highlighting issues and proposing viable solutions.

Findings

Singular behaviour can occur with $\\mathcal{L}_m=-\rho$ in late-time models.

Fully non-quasistatic equations can avoid divergences.

Choosing $\\mathcal{L}_m=p$ resolves issues in late-time regimes.

Abstract

The evolution of density perturbations is analysed in a modified theory of gravity with a nonminimal coupling between curvature and matter. We consider the broken degeneracy between the choices of matter Lagrangian for a perfect fluid, $\mathcal{L}_m=-\rho$ and $\mathcal{L}_m=p$, and determine the differences between their effects on the effective gravitational constant. We review the result for $\mathcal{L}_m=-\rho$ in the quasistatic approximation and show how it can lead to unphysical singular behaviour for late-time dominating models. This divergent regime can be avoided when considering the fully non-quasistatic perturbative equations, although the higher-order nature of the nonminimally coupled theory and the requirement of a physically viable effective gravitational constant strongly constrains the magnitude of these modifications to the action. We find that both of these issues can be removed when considering $\mathcal{L}_m=p$ at late times due to the pressureless nature of non-relativistic matter and provide predictions for inverse power-law models.