Speaker
Description
The f(R)-gravity represents the most straightforward extension of the General Relativity. Among the different possible formulations, the starting action can be selected using the Noether symmetry approach, a phisically motivated criterion based on Noether's theorem aimed at identifying viable models that exhibit symmetries. An advantage in applying such an approach is the reduction of the dynamical system and the associated minisuperspace, thus enabling the derivation of exact solutions to the equations of motion. In this study, we consider the f(R) gravity in a cosmological context and study the canonical and non canonical cases comparing the conserved quantities corresponding to symmetries in the selected models. For the non canonical case, we extend the Noether vector up to the second prolongation after finding out the transformation law for the second time derivative of fields that define our minisuperspace. The main goal is to understand if there are some differences both in the solutions of the Noether system and the corresponding conserved quantities comparing the two cases.