Nöther's symmetries and exact solutions in flat non-minimally coupled cosmological models

Abstract

Adopting the method described in previous papers, we search for Nöther's symmetries in point-like Friedman--Robertson--Walker (FRW) Lagrangians derived for general non-minimally coupled gravitational theories. We obtain exact solutions for flat models capable of producing inflation and recovering the Einstein regime at the present time (i.e. the scalar field and the coupling become constants directly related to the Newton constant ).