A non-singular universe with torsion

Kopczyński, Wojciech

doi:10.1016/0375-9601(72)90714-1

Cited by 140 publications

(120 citation statements)

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“…Thus the canonical energy-momentum tensor is symmetric if the acceleration of the fluid is zero [5]. Assuming spherical symmetry for the spin implies that S ij has only one nonvanishing component [13], S 23 = K, where K is a function of r. Since a static configuration is also assumed u i = δ i 0 and hence s 0 23 = K. Therefore, one can solve (6) and one finds…”

Section: Static Spherically Symmetric Spacetimementioning

confidence: 99%

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

Böhmer¹

2004

Class. Quantum Grav.

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In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory.The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.

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Section: Static Spherically Symmetric Spacetimementioning

confidence: 99%

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

Böhmer¹

2004

Class. Quantum Grav.

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“…The conservation law (12) implies that s 2 scales with the cosmic scale factor as ∼ a −6 , whereas ǫ (in the early, ultrarelativistic Universe) scales as ∼ a −4 . Torsion therefore prevents the collapsing spin-fluid matter from reaching a singularity [10,12] (the avoidance of singularities for matter composed of oriented spins has been shown in [13]). Instead, the Universe has a minimum but finite scale factor at which κs 2 /4 = ǫ.…”

mentioning

confidence: 98%

“…In GR, Ω S0 does not appear in (13), so Ω tends to 1 as a → 0, introducing the flatness problem in big-bang cosmology because Ω at the GUT epoch must have been tuned to 1 to a precision of more than 52 decimal places in order for Ω to be near 1 today. The horizon problem is related to the above flatness problem.…”

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confidence: 99%

Cosmological consequences of gravity with spin and torsion

Popławski¹

2013

Astronomical Review

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We show that the Einstein-Cartan-Sciama-Kibble theory of gravity with torsion not only extends general relativity to account for the intrinsic spin of matter, but it may also eliminate major problems in gravitational physics and answer major questions in cosmology. These problems and questions include: the origin of the Universe, the existence of singularities in black holes, the nature of inflation and dark energy, the origin of the matter-antimatter asymmetry in the Universe, and the nature of dark matter.The big-bang cosmology, based on Einstein's general theory of relativity (GR), successfully describes primordial nucleosynthesis and predicts the cosmic microwave background radiation. It does not, however, address some fundamental questions. What is the origin of the rapid expansion of the Universe from an initial, extremely hot and dense state? What is the nature of dark energy? And what caused the observed asymmetry between matter and antimatter in the Universe? The validity of GR also breaks inside black holes and at the beginning of the big bang, where the matter is predicted to compress indefinitely to curvature singularities. The big-bang cosmology also requires an inflationary scenario with additional fields to explain why the present Universe appears spatially flat, homogeneous and isotropic. In this essay, we briefly describe how the solution to the above questions and problems may come from an old adaptation of GR, the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity [1][2][3]. This classical theory naturally extends GR to account for the quantum-mechanical, intrinsic angular momentum (spin) of elementary particles that compose gravitating matter, causing spacetime to exhibit a geometric property called torsion.The ECKS gravity is based on the gravitational Lagrangian density proportional to the curvature scalar, as in GR. This theory, however, removes the GR restriction of the affine connection Γ k i j be symmetric. Instead, the antisymmetric part of the connection S k ij = Γ k [i j] (torsion tensor) is regarded as a dynamical variable like the metric tensor g ik . Varying the total action for the gravitational field and matter with respect to the metric gives the Einstein equations that relate the curvature to the dynamical energy-momentum tensor T ik = (2/ √ −g)δL/δg ik , where L is the matter Lagrangian density and g = det(g ik ) [4]. These equations can be written in a GR form as G ik = κ(T ik + U ik ), where the source is the modified energy-momentum tensor with an additional term U ik quadratic in the torsion tensor. G ik is the standard Einstein tensor and κ = 8πG/c 4 . These equations can also be written as R ik − R j j g ik /2 = κθ ik , where R ik (Γ) is the Ricci tensor of the connection and θ ik is the canonical energy-momentum tensor.Varying the total action with respect to the torsion gives the Cartan equations [1-3],

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“…This behavior is significant in spin fluids at extremely high densities, even without spin polarization, leading to gravitational repulsion and avoidance of curvature singularities by violating the energy condition of the singularity theorems [8]. Trautman, Kuchowicz, and others have shown that such a repulsion replaces the big-bang singularity with a nonsingular big bounce, before which the Universe was contracting [10,11]. In contrast to spin fluids, Dirac spinors coupled to torsion enhance the energy condition for the formation of singularities [6,12].…”

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confidence: 99%

Nonsingular, big-bounce cosmology from spinor-torsion coupling

2012

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The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.

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A non-singular universe with torsion

Cited by 140 publications

References 1 publication

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

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

Cosmological consequences of gravity with spin and torsion

Nonsingular, big-bounce cosmology from spinor-torsion coupling

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