The separate-universe approach and sudden transitions during inflation

Abstract

The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the inhomogeneous universe on large scales. We show that the separate-universe approach fails on a finite range of super-Hubble scales at a sudden transition from slow roll to ultra-slow roll during inflation in the very early universe. Such transitions are a feature of inflation models giving a large enhancement in the primordial power spectrum on small scales, necessary to produce primordial black holes after inflation. We show that the separate-universe approach still works in a piece-wise fashion, before and after the transition, but spatial gradients on finite scales require a discontinuity in the homogeneous solution at the transition. We discuss the implications for the $\delta N$ formalism and stochastic inflation, which employ the separate-universe approximation.

24 pages plus appendices. 9 figures. v2: to appear in JCAP

References in corpus (68)

• Planck 2015 results. XIII. Cosmological parameters
• Reheating after Inflation
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• Primordial Black Holes as Dark Matter
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• Inflation Dynamics and Reheating
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• Cosmological Backgrounds of Gravitational Waves
• A new approach to the evolution of cosmological perturbations on large scales
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• A general proof of the conservation of the curvature perturbation
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• Primordial Black Holes as Dark Matter: Recent Developments
• Adiabatic and entropy perturbations from inflation
• Primordial Black Holes as a dark matter candidate
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Cosmological perturbations
• The inflationary prediction for primordial non-gaussianity
• Semiclassicality and Decoherence of Cosmological Perturbations
• Primordial black holes from single field models of inflation
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Duality Invariance of Cosmological Perturbation Spectra
• Primordial black hole dark matter from single field inflation
• Steepest growth of the power spectrum and primordial black holes
• Adiabatic Modes in Cosmology
• Higher order corrections to primordial spectra from cosmological inflation
• Correlation Functions in Stochastic Inflation
• Features and New Physical Scales in Primordial Observables: Theory and Observation
• Enhancement of superhorizon scale inflationary curvature perturbations
• Cosmological parameter estimation and the inflationary cosmology
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Primordial black holes and second order gravitational waves from ultra-slow-roll inflation
• Primordial Black Holes from a tiny bump/dip in the Inflaton potential
• Quantum-to-classical Transition of Cosmological Perturbations for Non-vacuum Initial States
• Primordial Black Holes from Inflation and Quantum Diffusion
• Conserved cosmological perturbations
• Inflation and Primordial Black Holes
• Ultra slow-roll inflation demystified
• Quantum Discord of Cosmic Inflation: Can we Show that CMB Anisotropies are of Quantum-Mechanical Origin?
• On the divergences of inflationary superhorizon perturbations
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Anatomy of single-field inflationary models for primordial black holes
• Dissecting the growth of the power spectrum for primordial black holes
• Logarithmic Duality of the Curvature Perturbation
• Planck scale black hole dark matter from Higgs inflation
• Stochastic inflation beyond slow roll
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Obstructions to Bell CMB Experiments
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Primordial Black Holes from Multifield Inflation with Nonminimal Couplings
• The attractive behaviour of ultra-slow-roll inflation
• No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
• Squeezed bispectrum and one-loop corrections in transient constant-roll inflation
• The scalar bi-spectrum in the Starobinsky model: The equilateral case
• Primordial black holes from single-field inflation: a fine-tuning audit
• Failure of the stochastic approach to inflation beyond slow-roll
• Primordial Black Hole Formation in Starobinsky's Linear Potential Model
• Discord and Decoherence
• Cancellation of quantum corrections on the soft curvature perturbations
• One-loop infrared rescattering by enhanced scalar fluctuations during inflation
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Stochastic non-attractor inflation
• Numerically modeling stochastic inflation in slow-roll and beyond
• Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
• Sharp inflaton potentials and bi-spectra: Effects of smoothening the discontinuity

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• Stochastic Inflation in General Relativity
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Quantum diffusion and large primordial perturbations from inflation
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Stochastic inflation with gradient interactions
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• Quantitative classicality in cosmological interactions during inflation
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Stochastic Inflation in Numerical Relativity
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• $\delta N$ formalism with gradient interactions
• Ultra slow-roll with a black hole
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
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