Matter density perturbations and effective gravitational constant in modified gravity models of dark energy

TL;DR

This paper derives equations for matter density perturbations in general modified gravity models of dark energy, providing solutions and analyzing differences from standard gravity to aid observational constraints.

Contribution

It presents a general framework for matter perturbations in f(R, phi, X) models and relates scalar-tensor models to coupled dark energy scenarios, including analytical solutions.

Findings

Perturbation growth rates differ significantly from Einstein gravity in certain f(R) models.

Analytical solutions for matter perturbations are obtained for specific models.

The evolution of perturbations is estimated in both Jordan and Einstein frames.

Abstract

We derive the equation of matter density perturbations on sub-horizon scales for a general Lagrangian density f(R, phi, X) that is a function of a Ricci scalar R, a scalar field phi and a kinetic term X=-(nabla phi)^2/2. This is useful to constrain modified gravity dark energy models from observations of large-scale structure and weak lensing. We obtain the solutions for the matter perturbation delta_m as well as the gravitational potential Phi for some analytically solvable models. In a f(R) dark energy model with the Lagrangian density f(R)=alpha R^{1+m}-Lambda, the growth rates of perturbations exhibit notable differences from those in the standard Einstein gravity unless m is very close to 0. In scalar-tensor models with the Lagrangian density f=F(phi)R+2p(phi,X) we relate the models with coupled dark energy scenarios in the Einstein frame and reproduce the equations of perturbations known in the current literature by making a conformal transformation. We also estimate the evolution of perturbations in both Jordan and Einstein frames when the energy fraction of dark energy is constant during the matter-dominated epoch.