Related papers: Stochastic non de Sitter Inflation
We develop a stochastic approach to a non de Sitter Universe in a gauge-invariant way and obtain a system of Langevin-type equations which may be considered to be renormalization group equations for the long wave parts of the scalar fields…
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 investigate when effective theories of a scalar field on (quasi-)de Sitter background break down through the stochastic formalism. We derive the Fokker-Planck equation leaving the second order time derivative of the scalar field.…
We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations…
A long-standing problem in primordial cosmology is to understand the precise relation between the stochastic formalism and standard perturbation theory for light scalar fields in inflationary spacetimes. A complete correspondence between…
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 prove that the stochastic and standard field-theoretical approaches produce exactly the same results for the amount of light massive scalar field fluctuations generated during inflation in the leading order of the slow-roll…
We construct analytic and numerical solutions of the Fokker-Planck equation that arises in the context of stochastic inflation. We use these solutions to derive necessary conditions for eternal inflation on the higher derivatives of the…
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 reinterpret Starobinsky's stochastic inflation as an open quantum system, where short-wavelength modes act as the environment for long-wavelength modes. Using the Schwinger-Keldysh formalism, we systematically trace out the environment…
We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point…
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…
Cosmic inflation may exhibit stochastic periods during which quantum fluctuations dominate over the semi-classical evolution. Extracting observables in these regimes is a notoriously difficult program as quantum randomness makes them fully…
We investigate the range of inflationary universe models driven by scalar fields possessing a general interaction potential of the form $V(\phi) = V_0 \phi^n \exp(-\lambda \phi^m)$. Power-law, de Sitter and intermediate inflationary…
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 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…
We extend the formalism of stochastic inflation to the setup of non-attractor inflation with a sound speed $c_s$. We obtain the Langevin equations for the superhorizon perturbations and calculate the stochastic corrections to curvature…
Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the…
A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the…
For very general scalar-field theories in which the equations of motion are at second-order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of…