$f(R)$ gravity modifications: from the action to the data

Understand

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.