General vacuum-universe solutions in Brans-Dicke cosmology

Abstract

By a rescalation of the scalar field ϕ of the Jordan-Brans and Dicke cosmology, the general solutions of the Friedmannian ‘vacuum’ Universe are obtained. Only the flat space solution was previously known. Each solution is caracterized by the sign of the second time derivative of the rescaled field ψ≡ϕR ³ (R being the scale factor of the Robertson-Walker line-element):$\ddot \psi$ = 0 (flat space),$\ddot \psi$ < 0 (closed space), and$\ddot \psi$ > 0 (open space), so that the solutions are mutually exclusive. Of these, the open space one is damped-oscillatory andR attains its absolute minimum, equal to zero, in only one of the two ‘extreme’ cycles. Otherwise,R min remains positive. If the ϕ-field is dominant near the singularity, these solutions may have physical significance.

Also obtained, by the method mentioned above, is the general flat space solution for a ‘dust’ Universe and from it a closed space ‘dust’ solution. Both were found before by different authors, each one using a different method and, therefore, seemed up to now unrelated.