A new non-perturbative time-dependent string configuration

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.