STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

TL;DR

This paper investigates conditions under which stationary probability distributions can exist in Brans-Dicke inflationary cosmology, highlighting the roles of non-minimal coupling and radiative corrections in stabilizing the inflationary dynamics.

Contribution

It demonstrates that non-minimal conformal coupling and radiative corrections can induce stationary solutions in Brans-Dicke inflation, contrasting with the non-stationary behavior in standard chaotic inflation.

Findings

Non-minimal conformal coupling can provide a dynamical cutoff.

Radiative corrections may generate stationary probability distributions.

Large nonperturbative jumps are suppressed in Brans-Dicke theory.

Abstract

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.