Linear and non-linear perturbations in dark energy models

TL;DR

This work develops a comprehensive perturbation framework for dark energy models in which a scalar field couples explicitly to matter. It delivers general linear perturbation equations for a broad class of potentials and species-dependent couplings, derives a growth-bias relation, and shows how Yukawa corrections and density-dependent masses arise from the coupling. It further extends to second-order perturbations, deriving Newtonian-limit equations that incorporate coupling-induced corrections, laying the groundwork for non-linear analyses and N-body simulations. The results enable tests of coupled dark energy through deviations in growth, gravity on multiple scales, and non-linear clustering, with implications for precision cosmology and equivalence-principle investigations.

Abstract

I review the linear and second-order perturbation theory in dark energy models with explicit interaction to matter in view of applications to N-body simulations and non-linear phenomena. Several new or generalized results are obtained: the general equations for the linear perturbation growth; an analytical expression for the bias induced by a species-dependent interaction; the Yukawa correction to the gravitational potential due to dark energy interaction; the second-order perturbation equations in coupled dark energy and their Newtonian limit. I also show that a density-dependent effective dark energy mass arises if the dark energy coupling is varying.