Failure of the stochastic approach to inflation beyond slow-roll

Abstract

After giving a pedagogical review we clarify that the stochastic approach to inflation is generically reliable only at zeroth order in the (geometrical) slow-roll parameter ${\epsilon }_1$ if and only if ${\epsilon }_2^2\ll 6/{\epsilon }_1$, with the notable exception of slow-roll. This is due to the failure of the stochastic $\Delta N$ formalism in its standard formulation. However, by keeping the formalism in its regime of validity, we showed that, in ultra-slow-roll, the stochastic approach to inflation reproduces the power spectrum calculated from the linear theory approach.

arXiv commentv3: typo in the appendix corrected. Results unchanged. Published version in JCAP

References in corpus (21)

• Did LIGO detect dark matter?
• A new approach to the evolution of cosmological perturbations on large scales
• Formalising the Slow-Roll Approximation in Inflation
• Cosmic microwave background limits on accreting primordial black holes
• Horizon crossing and inflation with large η
• Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation
• Violation of non-Gaussianity consistency relation in a single field inflationary model
• Stochastic Quantum Gravitational Inflation
• Inflation with a constant rate of roll
• Correlation Functions in Stochastic Inflation
• Primordial Black Holes from Inflation and non-Gaussianity
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Quantum diffusion during inflation and primordial black holes
• Primordial Black Holes from Inflation and Quantum Diffusion
• Revisiting non-Gaussianity from non-attractor inflation models
• Quantum diffusion beyond slow-roll: implications for primordial black-hole production
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Stochastic approach to inflation II: classicality, coarse-graining and noises
• Perturbations in stochastic inflation
• The Graviton Tail almost Completely Wags the Dog
• Loop corrections to primordial non-Gaussianity

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