Probing the physical and mathematical structure of $f(R)$-gravity by PSR J0348 + 0432

There are several approaches to extend General Relativity in order to explain the phenomena related to the Dark Matter and Dark Energy. These theories, generally called Extended Theories of Gravity, can be tested using observations coming from relativistic binary systems as PSR J0348 + 0432. Using a class of analytical f(R)-theories, one can construct the first time derivative of orbital period of the binary systems starting from a quadrupolar gravitational emission. Our aim is to set boundaries on the parameters of the theory in order to understand if they are ruled out, or not, by the observations on PSR J0348 + 0432. Finally, we have computed an upper limit on the graviton mass showing that agree with constraint coming from other observations.