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

Matter density perturbations and effective gravitational constant in modified gravity models of dark energy - Astrophysics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We derive the equation of matter density perturbations on sub-horizon scalesfor a general Lagrangian density f(R, phi, X) that is a function of a Ricciscalar R, a scalar field phi and a kinetic term X=-(nabla phi)^2-2. This isuseful to constrain modified gravity dark energy models from observations oflarge-scale structure and weak lensing. We obtain the solutions for the matterperturbation delta m as well as the gravitational potential Phi for someanalytically solvable models. In a f(R) dark energy model with the Lagrangiandensity f(R)=alpha R^{1+m}-Lambda, the growth rates of perturbations exhibitnotable differences from those in the standard Einstein gravity unless m isvery close to 0. In scalar-tensor models with the Lagrangian densityf=F(phi)R+2p(phi,X) we relate the models with coupled dark energy scenarios inthe Einstein frame and reproduce the equations of perturbations known in thecurrent literature by making a conformal transformation. We also estimate theevolution of perturbations in both Jordan and Einstein frames when the energyfraction of dark energy is constant during the matter-dominated epoch.

Author: ** Shinji Tsujikawa**

Source: https://arxiv.org/