The separate-universe approach and sudden transitions during inflation

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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.
Original languageEnglish
Article number053
Number of pages35
JournalJournal of Cosmology and Astroparticle Physics
Issue number5
Publication statusPublished - 9 May 2024


  • cosmological perturbation theory
  • inflation
  • physics of the early universe
  • primordial black holes
  • UKRI
  • STFC
  • ST/T506345/1
  • ST/W001225/1

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