Related papers: The quantum Fokker-Planck equation of stochastic i…
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 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…
We generalize the stochastic approach to quasi-power-law inflationary Universes,obtain the corresponding Langevin and Fokker-Planck equations for the scalar field driving inflation and find stationary solutions to the above FP equation.
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 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 consider an infrared truncated massive minimally coupled scalar field with an asymmetric self-interaction $\frac{m^2}{2}\varphi^2\!+\!\frac{\lambda\varphi^4}{4!}\!+\!\frac{\beta\varphi^3}{3!}(\lambda\!>\!0)$ during a cosmological…
We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar…
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…
Understanding stochastic inflation, and in particular the systematic computation of controlled corrections from first principles, remains an important open problem. In this work, we address this problem from two complementary perspectives.…
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 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…
The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative than quantitative because…
We study the decoherence of massive fields during inflation based on the Zurek's density matrix approach. With the cubic interaction between inflaton and massive fields, the reduced density matrix for the massive fields can be calculated in…
We study the effects of the trans-Planckian dispersion relation on the spectrum of the primordial density perturbations during inflation. In contrast to the earlier analyses, we do not assume any specific form of the dispersion relation and…
The representation theory of de Sitter space allows for a category of partially massless particles which have no flat space analog, but could have existed during inflation. We study the couplings of these exotic particles to inflationary…
We study stochastic inflation in the presence of a dynamical gravitational constant. We describe the Arnowitt--Deser--Misner formalism for Jordan--Brans--Dicke theory of gravity with an inflaton field. The inflaton and dilaton scalar fields…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
We derive the semiclassical evolution of massless minimally coupled scalar matter in the de Sitter space-time from the Born-Oppenheimer reduction of the Wheeler-DeWitt equation. We show that the dynamics of trans-Planckian modes can be cast…
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…