Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches

Abstract

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 approximation. This is true both in the case for which this field is a test one and inflation is driven by another field, and the case for which the field plays the role of inflaton itself. In the latter case, in order to calculate the average of the mean square of the gauge-invariant inflaton fluctuation, the logarithm of the scale factor $a$ has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. The implications of particle production during inflation for the second stage of inflation and for the moduli problem are also discussed. The case of a massless self-interacting test scalar field in a de Sitter background with a zero initial renormalized mean square is also considered in order to show how the stochastic approach can easily produce results corresponding to diagrams with an arbitrary number of scalar field loops in the field-theoretical approach (explicit results up to 4 loops inclusive are presented).

Discussion expanded, references added, conclusions unchanged, matches the version to be published in Phys. Rev. D

References in corpus (6)

• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• On the divergences of inflationary superhorizon perturbations
• Towards a gauge invariant volume-weighted probability measure for eternal inflation
• Cosmological Measures without Volume Weighting
• Second Order Gauge-Invariant Perturbations during Inflation
• Back-reaction of Cosmological Fluctuations during Power-Law Inflation

Cited by in corpus (78)

• Inflation and Primordial Black Holes
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Electroweak Vacuum Stability in light of BICEP2
• Ultra-slow-roll inflation with quantum diffusion
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Spacetime Dynamics of a Higgs Vacuum Instability During Inflation
• Stochastic Inflation at NNLO
• Power spectrum in stochastic inflation
• Primordial black holes from stochastic tunnelling
• 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
• On Adiabatic Renormalization of Inflationary Perturbations
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Cosmological UV/IR Divergences and de-Sitter Spacetime
• Review on stochastic approach to inflation
• The Open Effective Field Theory of Inflation
• Markovian Dynamics in de Sitter
• Construction of inflationary scenarios with the Gauss-Bonnet term and nonminimal coupling
• Backreaction during inflation: a physical gauge invariant formulation
• WarmSPy: a numerical study of cosmological perturbations in warm inflation
• Backreaction in Cosmology
• The quantum Fokker-Planck equation of stochastic inflation
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Large fluctuations and Primordial Black Holes
• Numerical stochastic inflation constrained by frozen noise
• Stochastic non-attractor inflation
• Numerically modeling stochastic inflation in slow-roll and beyond
• Revisiting Magnetogenesis during Inflation
• Stochastic Inflation in General Relativity
• Stochastic Effects in Anisotropic Inflation
• Smooth coarse-graining and colored noise dynamics in stochastic inflation
• Unavoidable shear from quantum fluctuations in contracting cosmologies
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
• IR Divergence in Inflationary Tensor Perturbations from Fermion Loops
• Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs
• Early-Time Measure in Eternal Inflation
• Light scalars on cosmological backgrounds
• Feynman Rules for Stochastic Inflationary Correlators
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Stochastic inflation and primordial black holes
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Computing First-Passage Times with the Functional Renormalisation Group
• 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
• Tensor Mode Backreaction During Slow-roll Inflation
• 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
• Stochastic inflation with gradient interactions
• Stochastic Baryogenesis
• Inflation with Stochastic Boundary
• Non-Standard Primordial Clocks from Dynamical Mass in Alternative to Inflation Scenarios
• Stochastic approach to gravitational waves from inflation
• Spatial correlations of dark energy from quantum fluctuations in inflation
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Stochastic-tail of the curvature perturbation in hybrid inflation
• $\delta N$ formalism on the past light-cone
• Stochastic Inflation with Interacting Noises
• Stochastic Inflation in Numerical Relativity
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Time-reversed Stochastic Inflation
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Inflationary quantum dynamics and backreaction using a classical-quantum correspondence
• Deviations from Gaussian White Noise in Stochastic Inflation
• The hand-made tail: Non-perturbative tails from multifield inflation
• Power spectrum of stochastic wave and diffusion equations in the warm inflation models
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Testing Inflationary Cosmology
• A Tail of Eternal Inflation
• Stochastic quantum inflation for a canonical scalar field with linear self-interaction potential
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators
• Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta N$ formalism