The Einstein static universe with torsion and the sign problem of the cosmological constant

We study Einstein static universes in the context of generic f (R) models. It is shown that Einstein static solutions exist for a wide variety of modified gravity models sourced by a barotropic perfect fluid with equation of state w = p/ρ, but these solutions are always unstable to either homogeneous or inhomogeneous perturbations. Our general results are in agreement with specific models investigated in that past. We also discuss how our techniques can be applied to other scenarios in f (R) gravity.

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“…That is, all gradients of these quantities vanish in equations (18) and (20). These then simplify to…”

Section: B Perturbations About Constant Curvature Solutionsmentioning

confidence: 99%

Einstein static universes are unstable in genericf(R)models

Seahra

Böhmer

2009

Phys. Rev. D

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“…However, the spherical case with non-vanishing tangential pressure does not allow the construction of an anisotropic Einstein static universe with vanishing radial pressure. It should be noted that the Einstein static universe can be generalized to have non-constant pressure with two regular centers, see [17,18,20,21], and also in spacetimes with torsion an analog Einstein universe can be constructed, containing a constant radially symmetric torsion field [22]. It seems therefore that the anisotropic Einstein static universe is much more difficult to construct and it may possibly require a non-constant energy density.…”

Section: Presence Of a Cosmological Constantmentioning

confidence: 99%

A New Two-Sphere Singularity in General Relativity

Böhmer

2008

Int. J. Mod. Phys. D

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The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.

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“…However, this model suffers from a fine-tuning problem which can be ameliorated by modifying the cosmological field equations of the general relativity. For this reason, analogous static solutions and their stabilities have been studied in the context of the modified theories of gravity such as f (R) [24], f (T ) [25], Einstein-Cartan theory [26], massive gravity [27], Lyra geometry [28], loop quantum cosmology [29] and braneworld scenarios [30]. Stability of the Einstein static universe is also studied in the Horava-Lifshitz gravity [31].…”

Section: Introductionmentioning

confidence: 99%

Deformed Hořava–Lifshitz cosmology and stability of the Einstein static universe

2017

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Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Hořava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, k = 0. For the the special case of large values of running parameter of HL gravity ω, in a positively curved universe k > 0, the domination of the quintessence and phantom matter fields with barotropic equation of state parameter β < − is necessary while for a negatively curved universe k < 0, the matter fields with β > − 1 3 are needed to be the dominant fields of the universe. Also, a neutral stability against the vector perturbations is obtained. Finally, an inequality including the cosmological parameters of the Einstein static universe is obtained for the stability against the tensor perturbations. It turns out that for large ω values, there is a stability against the tensor perturbations.

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The Einstein static universe with torsion and the sign problem of the cosmological constant

Cited by 72 publications

References 24 publications

Einstein static universes are unstable in genericf(R)models

Einstein static universes are unstable in genericf(R)models

A New Two-Sphere Singularity in General Relativity

Deformed Hořava–Lifshitz cosmology and stability of the Einstein static universe

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