Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach

Abstract

The $\delta N$ formalism is a powerful approach to compute non-linearly the large-scale evolution of the comoving curvature perturbation $\zeta$. It assumes a set of FLRW patches that evolve independently, but in doing so, all the gradient terms are discarded, which are not negligibly small in models beyond slow-roll. In this Letter, we extend the formalism to capture these gradient corrections by encoding them in a homogeneous-spatial-curvature contribution assigned to each FLRW patch. For a concrete example, we apply this formalism to the ultra-slow-roll inflation, and find that it can correctly describe the large-scale evolution of the comoving curvature perturbation from the horizon exit. We also briefly discuss non-Gaussianities in this context.

6 pages main text, 2 pages end matter, 4 pages appendix, 3 figures. Form of the initial metric changed, clarifications added concerning the non-linear nature of the results, plot of the potential added, title changed, few minor changes added (main conclusions unchanged)

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Cited by in corpus (11)

• Stochastic inflation with gradient interactions
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• Inflationary relics from an Ultra-Slow-Roll plateau
• Curvature perturbations from kinetic preheating after $\alpha$-attractor inflation
• Stochastic Inflation in Numerical Relativity
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• $\delta N$ formalism with gradient interactions
• Separate universe in multifield inflation: a phase-space approach
• $\delta n$ formalism: A new formulation for the probability density of the curvature perturbation
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function