Stochastic approach to inflation: Classicality conditions

Abstract

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

Decoherence of gauge-invariant metric fluctuations during inflation

“…(The reader can see, for example, a stochastic treatment-but for matter field fluctuations-in ref. [3]. )…”

“…The inhomogeneous component φ( x, t) are the quantum fluctuations. The field that take into account only the modes with wavelengths larger than the now observable universe is called coarse-grained field and its dynamics is described by a second order stochastic equation [3].Stochastic inflation has played an important role in inflationary cosmology in the last two decades. This approach gives the possibility to make a description of the matter field fluctuations in the infrared (IR) sector by means of the coarse-grained matter field [2,4].…”

“…In the particular case where the tensor T αβ is diagonal, one obtains: χ = ψ [6]. I consider a semiclassical expansion for the scalar field ϕ( x, t) = φ c (t) + φ( x, t) [3], with expectation values 0|ϕ|0 = φ c (t) and 0|φ|0 = 0. Here, |0 is the vacuum state.…”

“…The inhomogeneous component φ( x, t) are the quantum fluctuations. The field that take into account only the modes with wavelengths larger than the now observable universe is called coarse-grained field and its dynamics is described by a second order stochastic equation [3].…”

Gauge invariant fluctuations of the metric during inflation from a new scalar-tensor Weyl-integrable gravity model

“…On the other hand, scalar fluctuations of the metric on cosmological scales can be studied in a non-perturbative formalism, describing not only small fluctuations, but the larger ones [12]. In this kind of model, it is assumed that the inflaton field exists at the beginning of the inflationary stage [13]. In view of this, it seems rather appealing and, perhaps, closer to the spirit of general relativity, to look for a model that explains the origin of the inflaton scalar field at a purely geometrical level.…”