Lie and Noether symmetry analysis in Brans–Dicke cosmology

Abstract

This paper is aimed to study the group invariant solutions of the evolution equations in Brans–Dicke cosmology. In this context, we have considered the flat homogeneous Brans–Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and have used Lie and Noether symmetry on the augmented system. From Lie symmetry we have determined the unknown potential for two different values of the equation of state parameter w. Then assuming that the Lagrangian admits a Noether symmetry, an analytic solution of the system is obtained in both old and new coordinate systems.