Can f(R) gravity contribute to (dark) radiation?

TL;DR

This paper explores whether modifications of f(R) gravity can account for dark radiation and cosmic acceleration, finding that such models can only minimally contribute to dark radiation without conflicting with observed matter power spectra.

Contribution

The study applies cosmographic and matter power spectrum analyses to constrain f(R) gravity models' ability to produce dark radiation, providing criteria for viable models.

Findings

f(R) gravity can only minimally contribute to dark radiation

Constraints from Planck data limit f(R) models to avoid disrupting matter power spectrum

Viable f(R) models must match small-scale structure observations

Abstract

We discuss the possibility that suitable modifications of gravity could account for some amount of the radiation we observe today, in addition to the possibility of explaining the present speed up of the universe. We start introducing and reviewing cosmological reconstruction methods for metric $f(R)$ theories of gravity that can be considered as one of the straightforward modifications of Einstein's gravity as soon as $f(R)\neq R$. We then take into account two possible $f(R)$ models which could give rise to (dark) radiation. Constraints on the models are found by using the Planck Collaboration 2015 data within a cosmographic approach and by obtaining the matter power spectrum of those models. The conclusion is that $f(R)$ gravity can only contribute minimally to the (dark) radiation to avoid departures from the observed matter power spectrum at the smallest scales (of the order of $0.01$Mpc$^{-1}$), i.e., precisely those scales that exited the horizon at the radiation dominated epoch. This result could strongly contribute to select reliable $f(R)$ models.