The stochastic approach to inflation relies on one key assumption, the emergence of a long-wave classical field that drives the inflation and is subject to a shortwave classical noise. In this work we consider explicitly the potential that acts on the inflaton field, and analyze classicality conditions that must be satisfied to have an effective classical stochastic approach. When these hold, the dynamics is given by a two-dimensional classical Fokker-Planck equation. We develop some examples, already widely considered in different approaches, and find a very suggestive result, which is the damping of the quantum fluctuations by the effect of the inflaton interaction potential. ͓S0556-2821͑96͒01624-4͔PACS number͑s͒: 98.80.Cq, 04.62.ϩv PHYSICAL REVIEW D

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner-Nordstr\"om black-hole is studied.Comment: 9 pages, no figures, improved versio

We propose a novel formalism for inflation from a 5D vacuum state which could explain both, seeds of matter and magnetic fields in the early universe. *

We develop a new approach to gravitational waves in which the Einstein equations are governed by the cosmological constant which is related to the existence of a manifold which is closed. We study an example in which the matter Lagrangian is described by the scalar (inflaton) field. There are only three dynamical solutions. In one of them the universe is initially static but begins to increase until an inflationary stage. We calculate the dynamics of GW in this primordial pre-inflationary stage of the universe. We found that there should be an infinite number of polarization modes in order to the fields can be quantized. Finally, we calculate the energy density due to the gravitational

In the framework of inflationary cosmology I study some aspects of nonequilibrium thermodynamics for the matter field fluctuations. The thermodynamic analysis is developed for de Sitter and power-law expansions of the universe. In both cases, I find that the heat capacity is negative leading respectively, to exponential and superexponential growth for the number of states in the infrared sector for de Sitter and power-law expansions of the universe. The spectrum for the matter field fluctuations can be understood from the background effective temperature at the horizon entry.

We discuss a semiclassical treatment to inflationary models from Kaluza-Klein theory without the cylinder condition. We conclude that the evolution of the early universe could be described by a geodesic trayectory of a cosmological 5D metric here proposed, so that the effective 4D FRW background metric should be a hypersurface on a constant fifth dimension. *

The warm inflation scenario is an alternative mechanism which can explain the isotropic and homogeneous Universe which we are living in. In this work I extend a previously introduced formalism, without the restriction of slow -roll regime. Quantum to classical transition of the fluctuations is studied by means of the "transition function" here introduced. I found that the fluctuations of radiation energy density decrease with time and the thermal equilibrium at the end of inflation holds. PACS number(s): 98.80. Cq, 05.40.+j Typeset using REVT E X

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