Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
Abstract
We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background LCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat LCDM parametrization though the radiation (w_eff=1/3), matter (w_eff=0) and deSitter (w_eff=-1) eras. b. Matter and radiation dominate during the `matter' and `radiation' eras respectively i.e. \Omega_m =1 when w_eff=0 and \Omega_r=1 when w_eff=1/3. We have found that the cosmological dynamical system constrained to obey the LCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f(R). One of them is the usual general relativistic form f(R)=R-2\Lambda. The other three forms in each era, reproduce the LCDM cosmic history but they do not satisfy requirement b. stated above. Only one of these forms (different from general relativity) is found to be an attractor of the dynamical cosmological evolution. It has (\Omega_DE=1, \Omega_r=0, \Omega_m=0) throughout the evolution. Its phase space trajectory is numerically obtained.
Keywords
Cite
@article{arxiv.gr-qc/0703006,
title = {Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?},
author = {S. Fay and S. Nesseris and L. Perivolaropoulos},
journal= {arXiv preprint arXiv:gr-qc/0703006},
year = {2008}
}
Comments
Minor Modifications. Accepted in Phys. Rev. D (to appear). 11 revtex pages, 6 figures. The mathematica files with the numerical analysis of the paper can be found at http://leandros.physics.uoi.gr/frlcdm/frlcdm.htm