Quantum gravity at very high energies

The problem of time and the quantization of three-dimensional gravity in th e strong coupling regime is studied following path integral methods. The ti me is identified with the volume of spacetime. We show that the effective a ction describes an infinite set of massless relativistic particles moving i n a curved three-dimensional target space, i.e., a tensionless 3-brane on a curved background. If the cosmological constant is zero the target space i s flat and there is no "graviton" propagation (i.e., G[g(ij)(2), g(ij)(1)] = 0). If the cosmological constant is different from zero, 3D gravity is bo th classical and quantum mechanically soluble. Indeed, we find the followin g results: (i) the general exact solutions of the Einstein equations are si ngular at t = 0 showing the existence of a big-bang in this regime and (ii) the propagation amplitude between two geometries <g(ij)(2), t(2)\g(ij) (1) , t(1)> vanishes as t --> 0, suggesting that big-bang is suppressed quantum mechanically. This result is also valid for D > 3. (C) 2001 Published by E lsevier Science B.V.