Standard cosmological evolution in a wide range off(R)models

Abstract

Using techniques from singular perturbation theory, we explicitly calculate the cosmological evolution in a class of modified gravity models. By considering both the CDTT and modified CDTT (mCDTT) models, which aims to explain the current acceleration of the universe with a modification of gravity, we show that Einstein evolution can be recovered for most of cosmic history in at least one $f(R)$ model. We show that a standard epoch of matter domination can be obtained in the mCDTT model, providing a sufficiently long epoch to satisfy observations. We note that the additional inverse term will not significantly alter standard evolution until today and that the solution lies well within present constraints from big bang nucleosynthesis. For the CDTT model, we analyze the ``recent radiation epoch'' behavior ($a\ensuremath{\propto}{t}^{1/2}$) found by previous authors. We finally generalize our findings to the class of inverse power-law models. Even in this class of models, we expect a standard cosmological evolution, with a sufficient matter domination era, although the sign of the additional term is crucial.