Related papers: Functional Approach to Stochastic Inflation
In the phase space perspective, scalar field slow roll inflation is described by a heteroclinic orbit from a saddle type fixed point to a final attractive point. In many models the saddle point resides in the scalar field asymptotics, and…
We present a replica field-theoretic approach to stochastic inflation in which a manifestation of dimensional reduction is found. The scale above which the latter dominates grows exponentially fast with time and thus affects largest…
The stochastic formalism of inflation allows us to describe the scalar-field dynamics in a non-perturbative way. The correspondence between the diffusion and Schr\"{o}dinger equations makes it possible to exhaustively construct analytical…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
In this paper, we compare dispersions of a scalar field in Euclidean quantum gravity with stochastic inflation. We use Einstein gravity and a minimally coupled scalar field with a quadratic potential. We restrict our attention to small mass…
In this paper we present a path integral formulation of stochastic inflation, in which volume weighting can easily be implemented. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how…
I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the…
The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for…
We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on…
We examine inflationary universe models driven by scalar fields with logarithmic potentials of the form $V(\phi) = V_0 \phi^p(\ln \phi)^q$. Combining the slow-roll approximation with asymptotic techniques, we identify regions of the…
We apply Starobinsky's formalism of stochastic inflation to the case of a minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and obtain analytical expressions…
We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin…
Stochastic inflation rests on the separate-universe approximation, i.e. the ability to describe long-wavelength fluctuations in an inflating universe as homogeneous perturbations of its background dynamics. Although this approximation is…
Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it…
We give a pedagogical review of the application of field theoretic and path integral methods to calculate moments of the probability density function of stochastic differential equations perturbatively.
Stochastic description of inflationary spacetimes emulates the growth of vacuum fluctuations by an effective stochastic ``noise field'' which drives the dynamics of the volume-smoothed inflaton. We investigate statistical properties of this…
Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation…
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous…
In our previous paper, we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the…
In this paper we develop the formalism for the stochastic approach to inflation at all order in slow-roll parameters. This is done by including the momentum and Hamiltonian constraints into the stochastic equations. We then specialise to…