Analytic solutions of Brans–Dicke cosmology: Early inflation and late time accelerated expansion

Abstract

In this paper, we investigate the most general exact solutions of Brans–Dicke cosmology by choosing the scale factor “a” as the new independent variable. It is shown that a set of three field equations can be reduced to a constraint equation and a first-order linear differential equation. Thus this new set of equations is solvable when one supplies one of the following pairs of functions: ([Formula: see text], [Formula: see text]), ([Formula: see text], [Formula: see text]) or ([Formula: see text], [Formula: see text]). A universe with a single component energy-matter density, the early universe with constant energy density and radiation and the present universe with constant energy density and matter are studied. It is seen that in all cases initial values of the universe cause [Formula: see text] potential and a constant term in the Hubble function which causes an exponential expansion of the universe. The relation between cosmological constant and initial values of the universe is found.