Noncritical Liouville string escapes constraints on generic models of quantum gravity

It has recently been pointed out that generic models of quantum gravity mustcontend with severe phenomenological constraints imposed by gravitationalCerenkov radiation, neutrino oscillations and the cosmic microwave backgroundradiation. We show how the non-critical Liouville-string model of quantumgravity we have proposed escapes these constraints. It gives energeticparticles subluminal velocities, obviating the danger of gravitational Cerenkovradiation. The effect on neutrino propagation is naturally flavour-independent,obviating any impact on oscillation phenomenology. Deviations from the expectedblack-body spectrum and the effects of time delays and stochastic fluctuationsin the propagation of cosmic microwave background photons are negligible, asare their effects on observable spectral lines from high-redshift astrophysicalobjects.Comment: 15 pages LaTeX, 2 eps figures include