Kinematics of Einstein-Cartan universes

Pasmatsiou, Klaountia; Tsagas, Christos G.; Barrow, John D.

doi:10.1103/physrevd.95.104007

Cited by 40 publications

(65 citation statements)

References 45 publications

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“…see [6,9]). In this study, we have adopted the definitions and the conventions of [10], which follow those of [8], though in the latter papers the metric signature is (+, −, −, −). Also note that the tildas will always indicate purely Riemannian (torsion free) variables.…”

Section: Field Equations and Bianchi Identitiesmentioning

confidence: 99%

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Friedmann-like universes with torsion

et al. 2019

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We consider spatially homogeneous and isotropic cosmologies with non-zero torsion. Given the high symmetry of these universes, we adopt a specific form for the torsion tensor that preserves the homogeneity and isotropy of the spatial surfaces. Employing both covariant and metric-based techniques, we derive the torsional versions of the continuity, the Friedmann and the Raychaudhuri equations. These formulae demonstrate how, by playing the role of the spatial curvature, or that of the cosmological constant, torsion can drastically change the evolution of the classic homogeneous and isotropic Friedmann universes. In particular, torsion alone can lead to exponential expansion. For instance, in the presence of torsion, the Milne and the Einstein-de Sitter universes evolve like the de Sitter model. We also show that, by changing the expansion rate of the early universe, torsion can affect the primordial nucleosynthesis of helium-4. We use this sensitivity to impose strong cosmological bounds on the relative strength of the associated torsion field, requiring that its ratio to the Hubble expansion rate lies in the narrow interval (−0.005813, +0.019370) around zero. Interestingly, the introduction of torsion can reduce the production of primordial helium-4, unlike other changes to the standard thermal history of an isotropic universe. Finally, turning to static spacetimes, we find that there exist torsional analogues of the classic Einstein static universe, with all three types of spatial geometry. These models can be stable when the torsion field and the universe's spatial curvature have the appropriate profiles.Since then, the EC theory (also known as ECKS theory) has been formally established and has received considerable recognition, as it provides the simplest classical extension of Einstein's general relativity (see [3] for a recent review and references therein).The EC theory postulates an asymmetric affine connection for the spacetime, in contrast to the symmetric Christoffel symbols of Riemannian spaces. In technical terms, torsion is described by the antisymmetric part of the non-Riemannian affine connection [1]. Therefore, in addition to the metric tensor, there is an independent torsional field, which also contributes to the total gravitational "pull". Geometrically speaking, curvature reflects the fact that the parallel transport of a vector along a closed loop in a Riemannian space depends on the path. The presence of torsion adds extra complications, since the aforementioned loop does not necessarily close. In a sense, curvature forces the spacetime to bend and torsion twists it. Dynamically, spacetime torsion is triggered by the intrinsic angular momentum (spin) of the matter, whereas spacetime curvature is caused by the mere presence of matter. This distinction is reflected in two sets of formulae, known as the Einstein-Cartan and the Cartan field equations.The literature contains a number of suggestions for experimentally testing gravitational theories with non-zero torsion (see [4] for a representativ...

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Section: Field Equations and Bianchi Identitiesmentioning

confidence: 99%

“…The rate of convergence/divergence of a worldline congruence is governed by the Raychaudhuri equation. In the presence of torsion, the latter reads [10]…”

Section: Kinematicsmentioning

confidence: 99%

Friedmann-like universes with torsion

et al. 2019

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“…A recent review on Friedmann cosmological models in Einstein-Cartan framework is done in [17]. The kinematics of cosmological spacetimes with nonzero torsion in the context of classical Einstein-Cartan gravity is given by [18] and the first derivation of FRW equations with torsion was presented in [19].…”

Section: Introductionmentioning

confidence: 99%

Acceleration in Friedmann cosmology with torsion

et al. 2019

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A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single φ(t) function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with φ(t) = −αH(t) ρ m (t)/ρ 0c n is totally compatible with recent cosmological data, where α and n are free parameters to be constrained from observations, ρ m is the matter energy density and ρ 0c the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about 0.65.

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“…Indeed, a similar effect occurs in the Raychaudhuri equation by the vorticity. This can be verified by the Raychaudhuri equation in the Einstein-Cartan universes obtained in [172] as…”

Section: Appendix Bmentioning

confidence: 75%

“…Therefore, here we just need to check that can we find such a null surface in the context of Einstein-Cartan theory or not. To answer this question, we refer to the Raychaudhuri equation in the Einstein-Cartan universes as obtained in the last section of [172]. Following the authors of [172], the effect of spin fluid can be highlighted further if we momentarily consider the familiar general-relativistic scenario of purely gravitational forces acting on an irrotational and shear-free perfect fluid with spin.…”

Section: Appendix Cmentioning

confidence: 99%

Emergent cosmos in Einstein–Cartan theory

et al. 2018

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Based on Padmanabhan's proposal, the accelerated expansion of the universe can be driven by the difference between the surface and bulk degrees of freedom in a region of space, described by the relation dV /dt = N sur − N bulk where N sur and N bulk = −N em + N de are the degrees of freedom assigned to the surface area and the matter-energy content inside the bulk such that the indices "em" and "de" represent energy-momentum and dark energy, respectively. In the present work, the dynamical effect of the Weyssenhoff perfect fluid with intrinsic spin and its corresponding spin degrees of freedom in the framework of Einstein-Cartan (EC) theory are investigated. Based on the modification of Friedmann equations due to the spin-spin interactions, a correction term for Padmanabhan's original relation dV /dt = N sur +N em −N de including the number of degrees of freedom related with these spin interactions is obtained through the modification in N bulk term as N bulk = −N em + N spin + N de leading to dV /dt = N sur + N em − N spin − N de in which N spin is the corresponding degrees of freedom related with the intrinsic spin of the matter content of the universe. Moreover, the validity of the unified first law and the generalized second law of thermodynamics for the Einstein-Cartan cosmos are investigated. Finally, by considering the covariant entropy conjecture and the bound resulting from the emergent scenario, a total entropy bound is obtained. Using this bound, it is shown that the for the universe as an expanding thermodynamical system, the total effective Komar energy never exceeds the square of the expansion rate with a factor of 3 4π .

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Kinematics of Einstein-Cartan universes

Cited by 40 publications

References 45 publications

Friedmann-like universes with torsion

Friedmann-like universes with torsion

Acceleration in Friedmann cosmology with torsion

Emergent cosmos in Einstein–Cartan theory

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