  A time-dependent bosonic string configuration is discussed, in graviton and
dilaton backgrounds, leading to Weyl-symmetry beta-functions which are
homogeneous in X^0, to any order in alpha'. As a consequence, a string
reparametrization can always be implemented, such that beta functions can be
cancelled, to any order in alpha'. This non-perturbative conformal invariance
is valid for any target space dimension, and leads to a power law expanding
Universe, for which the power vanishes if a specific relation between the
dimension and dilaton amplitude holds. Finally, D=4 is the minimum dimension
(in the case of a spherical world sheet) for which this configuration is
consistent with a Wick rotation in a Minkowski target space.
