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

Consistent bounds for the simultaneous variations of fundamental constants in the standard model of fundamental interactions are obtained from astronomical, astrophysical, and geophysical data. These bounds exclude the Dirac large-number hypothesis and, in general, any theory demanding a large variation of the fundamental constants. They also impose severe constraints on Kaluza-Klein and superstring theories, and should be considered as strong tests of the equivalence principle.

It has been recently claimed that cosmologies with time dependent speed of light might solve some of the problems of the standard cosmological scenario, as well as inflationary scenarios. In this letter we show that most of these models, when analyzed in a consistent way, lead to large violations of charge conservation. Thus, they are severly constrained by experiment, including those where c is a power of the scale factor and those whose source term is the trace of the energy-momentum tensor. In addition, early Universe scenarios with a sudden change of c related to baryogenesis are discarded.Since one of the key hypothesis of special relativity is the frame independence of the velocity of light c, it is implied in this statement the time and space independence of this velocity. As well established that it may seem, this constancy principle has been recently contested [1,2] to provide an alternative account of the horizon, flatness and cosmological constant problems present in the standard big bang scenario. Instead of the superluminal expansion of the Universe present in inflationary scenarios, a period in which light traveled much faster than today would explain the homogeneity we see today in the Universe. Some cosmological models have also been analyzed afterwards [3,4] to test the dynamical viability of this scenario.These ideas are highly provocative, not only from the observational viewpoint but also from the conceptual one. Indeed one of the key aspects of Einstein equivalence principle is the time-independence of the so called "fundamental constants" of physics [5]. The replacement of these parameters by one or more dynamical fields can lead to time-as well as space-dependent local fundamental constants. Unification schemes such as superstring theories [6] and Kaluza-Klein theories [7] have cosmological solutions in which the low-energy fundamental constants are functions of time. Usually low-energy phenomena are * Fellow of FOMEC † Member of CONICET 1