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.

arXiv commentMinor changes, references added

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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