Non-perturbative $\delta N$

Abstract

We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions, and present simple expressions for observables such as the power spectrum and the reduced bispectrum, $f_{\mathrm{NL}}$. These take the same form as those of the usual $\delta N$ expressions, but with the derivatives of $N$ replaced by non-perturbative $\delta N$ coefficients. We test the validity of this expansion and argue that our expressions are particularly well suited for use with simulations.

12 pages, 7 figures, V4 has minor amendments to the text to match version that has been accepted for publication

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• Non-Gaussian Spikes from Chaotic Billiards in Inflation Preheating
• Lattice calculation of non-Gaussianity from preheating
• Critical Number of Fields in Stochastic Inflation
• Non-Gaussianity from massless preheating
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Cited by in corpus (6)

• The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
• Inflationary Butterfly Effect: Non-perturbative Dynamics From Small-Scale Features
• The primordial curvature perturbation from lattice simulations
• High-redshift Mini-haloes from Modulated Preheating
• Curvature perturbations from vacuum transition during inflation
• Curvature perturbations from preheating with scale dependence