ar X iv : g r - qc / 9 51 10 79 v 1 2 9 N ov 1 99 5 Statistical Mechanics and Quantum Cosmology ∗

ar X iv : g r - qc / 9 51 10 48 v 1 1 6 N ov 1 99 5 Two lectures on Two - Dimensional Gravity ∗

ar X iv : g r - qc / 9 31 10 23 v 1 1 4 N ov 1 99 3 Tunnelling geometries II . Reduction methods for functional determinants

The reduction algorithms for functional determinants of differential operators on spacetime manifolds of different topological types are presented, which were recently used for the calculation of the no-boundary wavefunction and the partition function of tunnelling geometries in quantum gravity and cosmology. PACS numbers: 04.60.+n, 03.70.+k, 98.80.Hw

ar X iv : g r - qc / 9 21 10 19 v 1 1 5 N ov 1 99 2 What can we learn from the study of non - perturbative quantum general relativity ?

I attempt to answer the question of the title by giving an annotated list of the major results achieved, over the last six years, in the program to construct quantum general relativity using the Ashtekar variables and the loop representation. A summary of the key open problems is also included.

ar X iv : g r - qc / 9 51 10 66 v 1 2 4 N ov 1 99 5 Scalar Field Inhomogeneous

Some exact solutions for the Einstein field equations corresponding to inhomogeneous G 2 cosmologies with an exponential-potential scalar field which generalize solutions obtained previously are considered. Several particular cases are studied and the properties related to generalized inflation and asymptotic behaviour of the models are discussed.

ar X iv : g r - qc / 9 91 10 87 v 1 2 2 N ov 1 99 9 1 Eternal inflation and the present universe

Eternally inflating universes can contain thermalized regions with different values of the cosmological parameters. In particular, the spectra of density fluctuations should be different, because of the different realizations of quantum fluctuations of the inflaton field. I discuss a general method for calculating probability distributions for such variable parameters and analyze the density fl...