Separate Universes beyond General Relativity

Abstract

We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreting the Einstein tensor as an effective stress energy tensor, the condition is that the effective stress energy comoves with freely falling synchronous observers who establish the local expansion, so that the local curvature is conserved. By matching the expansion history of these synchronous observers in cosmological simulations, one can establish and test consistency relations even in the nonlinear regime of modified gravity theories.

14 pages, revisions reflect PRD accepted version

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Cited by in corpus (10)

• Primordial Black Holes and Local Non-Gaussianity in Canonical Inflation
• Phenomenology of Modified Gravity at Recombination
• Scale-dependent bias and bispectrum in neutrino separate universe simulations
• Generalized Slow Roll in the Unified Effective Field Theory of Inflation
• Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-$\alpha$ forest power spectrum
• Spectral Distortion Anisotropy from Inflation for Primordial Black Holes
• Effective field theory of degenerate higher-order inflation
• Curvature Perturbations in the Effective Field Theory of Inflation
• Breaking the Single Clock Symmetry: measuring single-field inflation non-Gaussian features
• The Black Hole Window on Cosmic Inflation