Review on stochastic approach to inflation

Abstract

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 the stochastic framework to different inflationary scenarios, especially to those of interest for primordial black hole formation. During the derivation of the stochastic formalism, we will emphasise two aspects in particular: the difference between the separate universe approach and the true long wavelength limit of scalar inhomogeneities and the generically non-Markovian nature of the noises that appear in the stochastic equations.

Minor changes, references added

References in corpus (20)

• Resummation of Massive Gravity
• Primordial Black Holes and Slow-Roll Violation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Stochastic growth of quantum fluctuations during slow-roll inflation
• On the divergences of inflationary superhorizon perturbations
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Hybrid inflation along waterfall trajectories
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Power spectrum in stochastic inflation
• Statistics of coarse-grained cosmological fields in stochastic inflation
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Gradient expansion approach to nonlinear superhorizon perturbations
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Gradient expansion approach to nonlinear superhorizon perturbations II -- a single scalar field --
• Perturbations in stochastic inflation
• Killing vector fields and a homogeneous isotropic universe
• Introduction to Numerical Relativity
• Smooth coarse-graining and colored noise dynamics in stochastic inflation

Cited by in corpus (24)

• Stochastic constant-roll inflation and primordial black holes
• Large fluctuations and Primordial Black Holes
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Numerical stochastic inflation constrained by frozen noise
• Stochastic Inflation in General Relativity
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Thermodynamics and decay of de Sitter vacuum
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Non-perturbative analysis for a massless minimal quantum scalar with $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ in the inflationary de Sitter spacetime
• An Étude on the Regularization and Renormalization of Divergences in Primordial Observables
• An update on adiabatic modes in cosmology and $\delta$N formalism
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian Boundary
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Inflationary relics from an Ultra-Slow-Roll plateau
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Stochastic Inflation in Numerical Relativity
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced current
• $\delta N$ formalism with gradient interactions
• Deviations from Gaussian White Noise in Stochastic Inflation
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting