Analysis of the nonminimally coupled scalar field in the Palatini formalism by the Noether symmetry approach

Abstract

We analyze a scalar field nonminimally coupled to gravity in the context of a Universe described by the flat Friedmann-Robertson-Walker metric. The adopted model comprises a Universe filled by the scalar field and standard matter (dark and baryonic). The corresponding field equations are obtained through the Palatini formalism. From the action of the model in the flat Friedmann-Robertson-Walker space-time, a pointlike Lagrangian of first order is obtained and the Noether symmetry approach is applied to restrict the forms of the a priori undefined coupling and potential of the scalar field. We show that the massive scalar field is associated with a Noether symmetry of the model. Analytical cosmological solutions for this case are found and their respective importance for the description of the dark energy are discussed.