Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?

TL;DR

This paper investigates whether f(R) modified gravity theories can replicate the standard LCDM cosmology, identifying specific f(R) forms that produce the desired cosmic history and analyzing their stability and dynamical behavior.

Contribution

The study reconstructs f(R) functions consistent with LCDM background evolution and identifies a unique attractor solution different from general relativity.

Findings

One f(R) form acts as a stable attractor mimicking LCDM.

Multiple f(R) forms can reproduce LCDM history but are not all stable.

The attractor solution has a dark energy dominated universe with no matter or radiation.

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.