A Liouville string approach to microscopic time and cosmology

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.