Late time mild inflation (LTMI) proposes to solve the age of the universe problem and the discrepancy between locally and globally measured values of the Hubble parameter. However, the mechanism proposed to achieve LTMI is found to be physically pathological by applying the theory of tails for the solutions of wave equations in curved spaces. Alternative mechanisms for LTMI are discussed, and the relevance of scalar wave tails for cosmology is emphasized. * Also at Instituts Internationaux de Chimie et de Physique Solvay. 177 Int. J. Mod. Phys. D 1999.08:177-188. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/04/15. For personal use only. a Unfortunately, the terminology commonly used in the literature is misleading; it would be more appropriate to refer to the "Huygens' property" instead of the "Huygens' principle." Int. J. Mod. Phys. D 1999.08:177-188. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/04/15. For personal use only.

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A type of cosmological history that includes large-scale entropy production is proposed. These cosmologies are based on reinterpretation of the matter-energy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby including irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This point of view results from consideration of the thermodynamics of open systems in the framework of cosmology. It is shown that the second law of thermodynamics requires that space-time transforms into matter, while the inverse transformation is forbidden. It appears that the usual initial singularity associated with the big bang is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. This is exemplified in the framework of a simple phenomenological model that leads to a three-stage cosmology: the first drives the cosmological system from the initial instability to a de Sitter regime, and the last connects with the usual matter-radiation Robertson-Walker universe. Matter as well as entropy creation occurs during the first two stages, while the third involves the traditional cosmological evolution. A remarkable fact is that the de Sitter stage appears to be an attractor independent of the initial fluctuation. This is also the case for all the physical predictions involving the present RobertsonWalker universe. Most results obtained previously, in the framework of quantum field theory, can now be obtained on a macroscopic basis. It is shown that this description leads quite naturally to the introduction of primeval black holes as the intermediate stage between the Minkowski vacuum and the present matter-radiation universe. The instability at the origin of the universe is the result of fluctuations of the vacuum in which black holes act as membranes that stabilize these fluctuations. In short, black holes will be produced by an "inverse" Hawking radiation process and, once formed, will decompose into "real" matter through the usual Hawking radiation. In this way, the irreversible transformation of space-time into matter can be described as a phase separation between matter and gravitation in which black holes play the role of "critical nuclei." Section I. Introduction Very few physical theories are in such a paradoxical situation as cosmology. On the one hand, our universe is characterized by a considerable entropy content, mainly in the form of black body radiation. On the other hand, Einstein's equations are adiabatic and reversible, and consequently they cannot provide, by themselves, an explanation of the origin of cosmological entropy.As is well known, matter may be produced quantum mechanically in the framework of Einstein's equations. The energy of these produced particles is then extracted from that of the (classical) gravitational field (1-4...

We present a simple and thermodynamically consistent cosmology with a phenomenological model of quantum creation of radiation due to vacuum decay. Thermodynamics and Einstein's equations lead to an equation in which H is determined by the particle number N . The model is completed by specifying the particle creation rate Γ =Ṅ /N , which leads to a second-order evolution equation for H. We propose a simple Γ that is naturally defined and that conforms to the thermodynamical conditions: (a) the entropy production rate starts at a maximum; (b) the initial vacuum (for radiation) is a non-singular regular vacuum; and (c) the creation rate is initially higher than the expansion rate H, but then falls below H. The evolution equation for H then has a remarkably simple exact solution, in which a non-adiabatic inflationary era exits smoothly to the radiation era, without a reheating transition. For this solution, we give exact expressions for the cosmic scale factor, energy density of radiation and vacuum, temperature, entropy and super-horizon scalar perturbations.PACS numbers: 9880C, 9880H, 9530T, 0540