Related papers: A consistent formulation of stochastic inflation I…
Stochastic inflation is widely used as a framework to study scalar field perturbations on an inflationary spacetime in a classical manner. In Starobinsky's seminal work and most of the subsequent literature, stochastic inflation is driven…
We numerically investigate stochastic dynamics in cosmology by solving Langevin equations for Infrared (IR) modes with stochastic noises generated by Ultraviolet (UV) modes at the coarse-graining scale. By construction, the stochastic…
Inflationary models that contain a transient ultra-slow-roll phase can exhibit strong non-perturbative dynamics, making the usual perturbative treatment of cosmological fluctuations incomplete. In such regimes, quantum diffusion and the…
The formalism of stochastic inflation is a powerful tool for analyzing the backreaction of cosmological perturbations, and making precise predictions for inflationary observables. We demonstrate this with the simple $m^2\phi^2$ model of…
We revisit the time evolution of a flat and non-flat direction system during inflation. In order to take into account quantum noises in the analysis, we base on stochastic formalism and solve coupled Langevin equations numerically. We focus…
The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…
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…
The It\^{o} and Stratonovich approaches are two ways to integrate stochastic differential equations. Detailed knowledge of the origin of the stochastic noise is needed to determine which approach suits a particular problem. I discuss this…
We revisit the Lagrangian formulation of stochastic inflation, where the path-integral approach is employed to derive the Langevin equation governing the dynamics of long-wavelength fields, in contrast to the standard method where the…
We present a new, recursive approach to stochastic inflation which is self-consistent and solves multiple problems which plagued a certain number of previous studies, in particular in realistic contexts where the background spacetime is…
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…
In this work we generalize a previously developed semiclassical approach to inflation, devoted to the analysis of the effective dynamics of coarse-grained fields, which are essential to the stochastic approach to inflation. We consider…
We discuss the inflaton $\phi$ in an interaction with an infinite number of fields treated as an environment (noise) with a friction $\gamma^{2}>0$. In a Markovian approximation we obtain a stochastic wave equation (appearing also in the…
Several models of inflation employing a triplet of SU(2) vectors with spatially orthogonal vacuum expectation values (VEVs) have been recently proposed. One (tensor) combination $t$ of the vector modes is amplified in some momentum range…
Stochastic resonance is a phenomenon where the response signal to external driving is enhanced by environment noise. In quantum regime, the effect of environment is often intrinsically non-Markovian. Due to the combination of such…
During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinskii's…
Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…
The perturbative approach to stochastic inflation is used to determine the spectrum of density fluctuations and gravitational waves due to the coarse grained field. The amplitude of the curvature fluctuation spectrum, the spectral index and…
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation and giving references for the readers interested on results coming from the application of…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…