The cosmological model of Brans-Dicke theory

We use the generalized Brans-Dicke theory, in which the Pauli metric is identified to be the physical space-time metric, to study the Universe in different epochs. Exact analytical expressions for dilaton field sigma, cosmological radius R and density parameter Omega are obtained for k = +1,0,-1 Universe in the radiation-dominated epoch. For matter dominated Epoch, exact analytical expressions for Hubble parameter H, cosmological radius, dilaton field, deceleration factor q, density parameter and the gravitational coupling of the ordinary matter are obtained for the flat Universe. Other important results are: (1) the density parameter Omega is always less than unity for the flat Universe because the dilaton field plays a role as an effective dark matter, and (2) the new Brans-Dicke parameter omega must be larger than 31.75 in order to consistent with the observed data.