  In the non-critical string framework that we have proposed recently, the time
$t$ is identified with a dynamical local renormalization group scale, the
Liouville mode, and behaves as a statistical evolution parameter, flowing
irreversibly from an infrared fixed point - which we conjecture to be a
topological string phase - to an ultraviolet one - which corresponds to a
static critical string vacuum. When applied to a toy two-dimensional model of
space-time singularities, this formalism yields an apparent renormalization of
the velocity of light, and a $t$-dependent form of the uncertainty relation for
position and momentum of a test string. We speculate within this framework on a
stringy alternative to conventional field-theoretical inflation, and the decay
towards zero of the cosmological constant in a maximally-symmetric space.
