Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation

Abstract

It is well known that a coarse-grained scalar field living on a de~Sitter (dS) background exhibits classical stochastic behavior, driven by a noise whose amplitude is set by the Hubble constant $H$. The coarse-graining is achieved by discarding wave numbers larger than a cutoff $\sigma aH$ and demanding that $\sigma \ll 1$. Similar results hold for quasi-dS space, where the equation of state parameter $w$ is close to $-1$. Here we present exact expressions for the noise amplitude of a free massless field on an inflationary background with constant $w<-1/3$. We find that a classical stochastic behavior can emerge for $-5/3<w<-1/3$. Furthermore, as we move away from $w=-1$ and approach $w=-1/3$, the constraint $\sigma \ll 1$ is relaxed and larger cutoffs ($\sigma \sim 1$) become feasible, too. However, in general the amplitude of the noise depends on $\sigma$, except in the quasi-dS regime $w\approx -1$.

18 pages, 4 figures, typos fixed, matches the published version

References in corpus (23)

• Stochastic Inflationary Scalar Electrodynamics
• 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
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Ultra-slow-roll inflation with quantum diffusion
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• 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
• Stochastic Inflation at NNLO
• Power spectrum in stochastic inflation
• Primordial black holes from stochastic tunnelling
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Stochastic constant-roll inflation and primordial black holes
• Review on stochastic approach to inflation
• Stochastic inflation at all order in slow-roll parameters: foundations
• Perturbations in stochastic inflation
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Stochastic non-attractor inflation
• Stochastic Effects in Anisotropic Inflation
• Stochastic Effects in Axion Inflation and Primordial Black Holes Formation
• Inflation with Stochastic Boundary

Cited by in corpus (4)

• Stochastic Inflation with Interacting Noises
• Deviations from Gaussian White Noise in Stochastic Inflation
• Impact of conversion-driven processes on singlet-doublet Majorana dark matter relic
• $\delta n$ formalism: A new formulation for the probability density of the curvature perturbation