  We tudy flat Friedmann-Robertson-Walker cosmology in Brans-Dicke-type
theories 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 $\omega>-{3/2}$. It is
shown that the cosmological singularity occuring in the Einstein frame
formulation of this theory is removed in the Jordan frame in the range
$-{3/2}<\omega<\leq-{4/3}$. This result is interpreted in the ligth of a
viewpoint (first presented in reference gr-qc/9905071) 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.
