On Separate Universes
Liang Dai, Enrico Pajer, Fabian Schmidt

TL;DR
This paper proves the separate universe conjecture for certain density perturbations in $\\Lambda$CDM, generalizes it to scalar perturbations, and clarifies the implications for local non-Gaussianity and galaxy bias measurements.
Contribution
It provides a rigorous proof of the separate universe conjecture for spherical and general scalar perturbations, and clarifies the observational signatures of non-Gaussianity.
Findings
The separate universe conjecture holds for spherical compensated tophat perturbations.
The conjecture extends to scalar perturbations' isotropic part but not anisotropic parts.
Nonlinear gravitational dynamics do not produce observable local-type non-Gaussianity signals.
Abstract
(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in CDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
