Holes in the static Einstein universe and the model of the cosmological voids

Abstract

Spherically symmetric, static model of the cosmological voids is constructed in the framework of the Tolman-Oppenheimer-Volkov equation with the cosmological constant. Extension of the Tooper result (dimensionless form of the TOV equation) is provided for non-zero $\Lambda$. Then, the equation is simplified in $\alpha \to 0$, $\lambda \to 0$, $\lambda /\alpha =const$ regime, suitable for largest structures in $\Lambda$-dominated universe. Voids are treated as an underdensity regions in the static Einstein universe. Both overdensity and underdensity (relative to static universe) solutions exist. They are identified with standard astrophysical spherical objects and voids, respectively. Model is tested against observed properties (the radius - the central density relation) and density profiles of voids. Analytical formulae for radial density contrast profile and radii of the voids are derived. Some consequences for cosmological n-body simulations are suggested. Hints on the dark matter/dark energy EOS filling the voids are provided.

11 pages, 7 figures

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• On the linearity of tracer bias around voids
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• Cavity evolution in relativistic self-gravitating fluids
• Einstein Static Universe in Rastall Theory of Gravity
• The stability of Einstein static universe in the DGP braneworld
• Stability of the Einstein static universe in Einstein-Cartan theory
• Emergent scenario in the Einstein-Cartan theory
• Cosmic voids detection without density measurements
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• Emergent universe in spatially flat cosmological model
• Stability of Einstein static universe in gravity theory with a non-minimal derivative coupling
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• Analytical approximations for primordial power spectra in a spatially closed emergent universe
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• Elastic Planetoids
• Cosmic voids and BAO with relative baryon-CDM perturbations