2007/05/31 by Shinji Tsujikawa · 1 citation
Physics and Astronomy · #astro-ph #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.76.023514
published as Phys.Rev.D76:023514,2007 · 11 pages, no figures, typos are corrected, version to appear in Physical Review D
arxiv created 2007/11/06 · arxiv updated 2009/12/01
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 deltam 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 R1+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.