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arXiv · 2505.10291

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

Miguel Barroso Varela·Orfeu Bertolami
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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.

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Miguel Barroso Varela, Orfeu Bertolami. 2025-05-15. Density perturbations in nonminimally coupled gravity: symptoms of Lagrangian density ambiguity. https://doi.org/10.1088/1475-7516%2F2026%2F01%2F032

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