Brans-Dicke-type theories and avoidance of the cosmological singularity

Abstract

We study flat Friedmann-Robertson-Walker cosmology in a Brans-Dicke-type theory of gravitation with minimal coupling between the scalar field and the matter fields in the Einstein frame (general relativity with an extra scalar field) for arbitrary values of the Brans-Dicke parameter $\ensuremath{\omega}>\ensuremath{-}\frac{3}{2}.$ It is shown that the cosmological singularity occurring in the Einstein frame formulation of this theory is removed in the Jordan frame in the range $\ensuremath{-}\frac{3}{2}<\ensuremath{\omega}<~\ensuremath{-}\frac{4}{3}.$ This result is interpreted in the light of a viewpoint asserting that both Jordan frame and Einstein frame formulations of general relativity are physically equivalent. The implications of the obtained result for string theory are outlined.