Abstract
We study a stochastic formalism for a nonperturbative treatment of the inflaton field in the framework of a noncompact Kaluza–Klein (KK) theory during an inflationary (de Sitter) expansion, without the slow-roll approximation.
Highlights
Stochastic inflation model is one of the very few that solves almost all of the well-known cosmological problems
In this work we have developed a stochastic treatment for the effective 4D inflaton field from a KK theory of gravity without the hypothesis of a slow - roll regime
In this framework the long - wavelength modes of the inflaton field reduces to a quantum system subject to a quantum noise originated by the short - wavelength sector
Summary
Stochastic inflation model is one of the very few that solves almost all of the well-known cosmological problems. Fit the scaling spectrum predicted by the inflation model, suggests that they had their origin in the quantum fluctuations of the “inflaton” scalar field during the inflationary era. In principle this problem is of a quantal nature, the fact that under certain conditions—which are made precise in [1,2,3]—the inflaton field can be considered as classical largely simplifies the approach, by allowing a Langevin-like stochastic treatment. The most widely accepted approach assume that the inflationary phase is driving by a quantum scalar field φ with a potential V (φ) Within this perspective, the stochastic inflation proposes to describe the dynamics of this quantum field on the basis of a splitting of φ in a homogeneous and an inhomogeneous components. The idea that matter in four dimensions (4D) can be explained from a
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