A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
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Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
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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).
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The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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.
Two-loop Yukawa corrections in de Sitter yield ⟨ϕ²⟩ ~ ln⁴a at late times, with a resummed expression that is bounded, decreases with larger Yukawa coupling, and implies a growing dynamical scalar mass.
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.
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
citing papers explorer
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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
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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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Yukawa scalar self energy at two loop and $\langle \phi^2 \rangle$ in the inflationary de Sitter spacetime
Two-loop Yukawa corrections in de Sitter yield ⟨ϕ²⟩ ~ ln⁴a at late times, with a resummed expression that is bounded, decreases with larger Yukawa coupling, and implies a growing dynamical scalar mass.
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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.
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A Compact Story of Positivity in de Sitter
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.