  In the context of a cosmological string model describing the propagation of
strings in a time-dependent Robertson-Walker background space-time, we show
that the asymptotic acceleration of the Universe can be identified with the
square of the string coupling. This allows for a direct measurement of the
ten-dimensional string coupling using cosmological data. We conjecture that
this is a generic feature of a class of non-critical string models that
approach asymptotically a conformal (critical) sigma model whose target space
is a four-dimensional space-time with a dilaton background that is linear in
sigma-model time. The relation between the cosmic acceleration and the string
coupling does not apply in critical strings with constant dilaton fields in
four dimensions.
