Exact solutions for a scalar-tensor theory through symmetries

Abstract

In this paper, we study how to determine the unknown functions for the scalar tensor model f(R, φ) where the Ricci scalar is allowed to appear in a nonlinear way. The methods followed to determine these functions are: the matter collineation approach, the Lie group method and the Lagrangian collineation approach. We find several exact analytical solutions for a cosmological model with a FRW metric. We determine that some of the results are also valid for some anisotropic metric (e.g. the self-similar ones)