The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
Tomberg, Stochastic constant-roll inflation and pri- mordial black holes, Phys
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Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Multifield stochastic inflation: Relevance of number of fields in statistical moments
Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Higgs models.