$f(R)$ gravity modifications: from the action to the data
  It is a very well established matter nowadays that many modified gravity
models can offer a sound alternative to General Relativity for the description
of the accelerated expansion of the universe. But it is also equally well known
that no clear and sharp discrimination between any alternative theory and the
classical one has been found so far. In this work, we attempt at formulating a
different approach starting from the general class of $f(R)$ theories as test
probes: we try to reformulate $f(R)$ Lagrangian terms as explicit functions of
the redshift, i.e., as $f(z)$. In this context, the $f(R)$ setting to the
consensus cosmological model, the $\Lambda$CDM model, can be written as a
polynomial including just a constant and a third-order term. Starting from this
result, we propose various different polynomial parameterizations $f(z)$,
including new terms which would allow for deviations from $\Lambda$CDM, and we
thoroughly compare them with observational data. While on the one hand we have
found no statistically preference for our proposals (even if some of them are
as good as $\Lambda$CDM by using Bayesian Evidence comparison), we think that
our novel approach could provide a different perspective for the development of
new and observationally reliable alternative models of gravity.
