Lagrangian Formulation of Stochastic Inflation: A Recursive Approach

Abstract

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 taken to be dynamical, where there is more than one field present, especially with a mass hierarchy, or where the role played by back-reaction is suspected to be important. We first review the formalism of stochastic inflation as it is usually heuristically presented, that is, deriving the Langevin equations from the field equations of motion, and summarize previous results on the subject. We demonstrate where inconsistent approximations to the Langevin equations are commonly made, and show how these can be avoided. This set up shares many similarities with quantum Brownian motion and out-of-equilibrium statistical quantum dynamics. We hence review how path integral techniques can be applied to the stochastic inflationary context. We show this formalism to be consistent with the standard approach, develop a natural perturbative expansion, and use it to calculate the one-loop corrected Langevin equations.

27 pages, 6 figures

References in corpus (11)

• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Warm Inflation and its Microphysical Basis
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Pointer states for primordial fluctuations in inflationary cosmology
• Power spectrum for inflation models with quantum and thermal noises
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Perturbative Non-Equilibrium Thermal Field Theory
• Local Approximations for Effective Scalar Field Equations of Motion
• Perturbations in stochastic inflation
• Recursive Stochastic Effects in Valley Hybrid Inflation
• Analytical Study of Mode Coupling in Hybrid Inflation

Cited by in corpus (24)

• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Primordial Black Holes
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Effective long wavelength scalar dynamics in de Sitter
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Review on stochastic approach to inflation
• Backreaction and Stochastic Effects in Single Field Inflation
• The quantum Fokker-Planck equation of stochastic inflation
• Numerical stochastic inflation constrained by frozen noise
• Recursive Stochastic Effects in Valley Hybrid Inflation
• Thermal Interpretation of Infrared Dynamics in de Sitter
• Can Back-Reaction Prevent Eternal Inflation?
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• An Étude on the Regularization and Renormalization of Divergences in Primordial Observables
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll
• A theoretical model for electromagnetic characterization of a spherical dust molecular cloud equilibrium structure
• The hand-made tail: Non-perturbative tails from multifield inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function