Canf(R)modified gravity theories mimic aΛCDMcosmology?

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 {lambda}CDM cosmology. In particular we impose the following requirements: (a) A background cosmic history H(z) provided by the usual flat {lambda}CDM parametrization though the radiation (w{sub eff}=1/3), matter (w{sub eff}=0), and de Sitter (w{sub eff}=-1) eras. (b) Matter and radiation dominate during the ''matter'' and ''radiation'' eras, respectively, i.e. {omega}{sub m}=1 when w{sub eff}=0 and {omega}{sub r}=1 when w{sub eff}=1/3. We have found that the cosmological dynamical system constrained to obey the {lambda}CDM 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 {lambda}CDM cosmic history but they do not satisfy requirement (b) stated above.