Standard Cosmological Evolution in a Wide Range of f(R) Models

TL;DR

This paper investigates the cosmological evolution of a class of f(R) gravity models, demonstrating that standard matter-dominated epochs can be achieved, aligning with observations and constraints from Big Bang Nucleosynthesis.

Contribution

The study explicitly calculates cosmological evolution in f(R) models using singular perturbation theory, showing standard evolution can be recovered in inverse power-law models.

Findings

Standard matter domination can be achieved in the mCDTT model.

The inverse term does not significantly alter evolution until today.

Models are consistent with Big Bang Nucleosynthesis constraints.

Abstract

Using techniques from singular perturbation theory, we explicitly calculate the cosmological evolution in a class of modified gravity models. By considering the (m)CDTT model, 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 analyse the ``recent radiation epoch'' behaviour (a \propto t^{1/2}) found by previous authors. We finally generalise 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.