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

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.

25 pages, 2 figures, Matches published version in JCAP

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