Analytic Solutions of Brans-Dicke Cosmology: Early Inflation and Late Time Accelerated Expansion

Abstract

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: (φ(a), ρ(a)), (φ(a), V (a)) or (φ(a), H(a)). A universe with a single component energy-matter density is studied. It is seen that when there is no constant energy density, the Hubble function still contains a constant term which causes exponential expansion. This constant is expressed in terms of the initial values of the universe. An early universe and the present universe with dark energy are studied. In addition late time accelerated expansion is also explained with cosmic domain walls. If we take Brans-Dicke parameter w > 4 × 10 4 formulas of the Hubble function reduce to solutions of ΛCDM cosmology. Therefore comparison of our results with recent observations of type Ia supernovae indicates that eighty-nine percent of present universe may consist of domain walls while rest is matter.