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