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

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

2007-05-08

arxiv.org/abs/0705.1032v4

Phys.Rev.D76:023514,2007

Astronomy and Astrophysics

Astrophysics

11 pages, no figures, typos are corrected, version to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.76.023514

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.

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