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.

arXiv comment6 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)

References in corpus (59)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Non-Gaussianity from Inflation: Theory and Observations
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• A general proof of the conservation of the curvature perturbation
• The inflationary prediction for primordial non-gaussianity
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Non-Gaussianity of the primordial perturbation in the curvaton model
• Steepest growth of the power spectrum and primordial black holes
• Violation of non-Gaussianity consistency relation in a single field inflationary model
• Correlation Functions in Stochastic Inflation
• Enhancement of superhorizon scale inflationary curvature perturbations
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Primordial Black Holes from Inflation and non-Gaussianity
• Primordial Black Holes from Inflation and Quantum Diffusion
• Conserved cosmological perturbations
• A Single Field Inflation Model with Large Local Non-Gaussianity
• Primordial non-gaussianity up to all orders: theoretical aspects and implications for primordial black hole models
• Primordial black hole formation with non-Gaussian curvature perturbations
• Revisiting non-Gaussianity from non-attractor inflation models
• Primordial Black Holes for the LIGO Events in the Axion-like Curvaton Model
• Quantum diffusion beyond slow-roll: implications for primordial black-hole production
• Non-perturbative non-Gaussianity and primordial black holes
• The Formation Probability of Primordial Black Holes
• Ultra-slow-roll inflation with quantum diffusion
• Logarithmic Duality of the Curvature Perturbation
• Abundance of primordial black holes with local non-Gaussianity in peak theory
• Stochastic inflation beyond slow roll
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• In-in and $\delta N$ calculations of the bispectrum from non-attractor single-field inflation
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Stochastic Ultra Slow Roll Inflation
• On the slope of curvature power spectrum in non-attractor inflation
• The attractive behaviour of ultra-slow-roll inflation
• Non-Gaussian Formation of Primordial Black Holes: Effects on the Threshold
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Peaks and primordial black holes: the effect of non-Gaussianity
• One Small Step for an Inflaton, One Giant Leap for Inflation: a novel non-Gaussian tail and primordial black holes
• δN Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum
• Primordial Black Hole Formation in Starobinsky's Linear Potential Model
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Primordial Black Hole Formation in Non-Minimal Curvaton Scenario
• Stochastic constant-roll inflation and primordial black holes
• The separate-universe approach and sudden transitions during inflation
• Solving peak theory in the presence of local non-gaussianities
• Growth of curvature perturbations for PBH formation \& detectable GWs in non-minimal curvaton scenario revisited
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Formation of trapped vacuum bubbles during inflation, and consequences for PBH scenarios
• Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations
• The Primordial Black Hole Abundance: The Broader, the Better
• Curvaton in large field inflation
• Uphill inflation
• Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes
• Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Anisotropic separate universe and Weinberg's adiabatic mode
• \bf $\delta M$ Formalism and Anisotropic Chaotic Inflation Power Spectrum
• Hamiltonian formalism for cosmological perturbations: fixing the gauge

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