Symmetry analysis and exact solutions of modified Brans-Dicke cosmological equations

We perform a symmetry analysis of modified Brans-Dicke cosmological equations and present exact solutions. We discuss how the solutions may help to build models of cosmology where, for the early universe, the expansion is linear and the equation of state just changes the expansion velocity but not the linearity. For the late universe the expansion is exponential and the effect of the equation of state on the rate of expansion is just to change the constant Hubble parameter.