Exact scalar–tensor cosmological models

Abstract

Scalar–tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the universe. In the present paper, we investigate the cosmological solution of a scalar–tensor gravitational theory, in which the scalar field [Formula: see text] couples to the geometry via an arbitrary function [Formula: see text]. The kinetic energy of the scalar field as well as its self-interaction potential [Formula: see text] are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman–Robertson–Walker universe in the framework of the scalar–tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the universe.