Does spatial flatness forbid the turnaround epoch of collapsing structures?
Abstract
Cosmological observational analysis frequently assumes that the Universe is spatially flat. We aim to nonperturbatively check the conditions under which a flat or nearly flat expanding dust universe, including the Λcolddarkmatter (ΛCDM) model if interpreted as strictly flat, forbids the gravitational collapse of structure. We quantify spatial curvature at turnaround. We use the Hamiltonian constraint to determine the pointwise conditions required for an overdensity to reach its turnaround epoch in an exactly flat spatial domain. We illustrate this with a planesymmetric, exact, cosmological solution of the Einstein equation, extending earlier work. More generally, for a standard initial power spectrum, we use the relativistic Zel'dovich approximation implemented in INHOMOG to numerically estimate how much positive spatial curvature is required to allow turnaround at typical epochs/length scales in almostEinsteinde Sitter (EdS)/ΛCDM models with inhomogeneous curvature. We find that gravitational collapse in a spatially exactly flat, irrotational, expanding, dust universe is relativistically forbidden pointwise. In the spatially flat planesymmetric model considered here, pancake collapse is excluded both pointwise and in averaged domains. In an almostEdS/ΛCDM model, the perdomain average curvature in collapsing domains almost always becomes strongly positive prior to turnaround, with the expansionnormalised curvature functional reaching Ω_{Script R}^{Script D}~5. We show analytically that a special case gives Ω_{Script R}^{Script D}=5 exactly (if normalised using the EdS expansion rate) at turnaround. An interpretation of ΛCDM as literally 3Ricci flat would forbid structure formation. The difference between relativistic cosmology and a strictly flat ΛCDM model is fundamental in principle, but we find that the geometrical effect is weak.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 December 2019
 DOI:
 10.1088/14757516/2019/12/049
 arXiv:
 arXiv:1902.09064
 Bibcode:
 2019JCAP...12..049R
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 38 pages