Physical aspects of the space–time torsion

Torsion-induced bounces have been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsion-supported bounce.

“Torsion-induced bounces have also been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsionsupported bounce [11-13, 22, 28, 29].”

In a microscopic Einstein-Cartan treatment, the spin-torsion contribution for a fermion fluid can be written schematically as ρs ∼ ξ n^2 / M_Pl^2, where n is the fermion number density and ξ = O(1) depends on spin representation and conventions.

“In a microscopic Einstein-Cartan treatment, the spintorsion contribution for a fermion fluid can be written schematically as ρ s ∼ ξ n 2 M 2 Pl , (45 ) where n is the fermion number density and ξ = O(1) depends on spin representation and conventions [11][12][13]33].”

The -ρs term in the Friedmann equation and the -2ρs term in the Raychaudhuri equation follow directly from the algebraic Einstein-Cartan/Weyssenhoff reduction, rather than from an added sign choice.

“So the -ρ s term in Friedmann and the -2ρ s term in Raychaudhuri follow directly from the algebraic Einstein-Cartan/Weyssenhoff reduction, rather than from an added sign choice [11][12][13].”

In EC theory, algebraically eliminating torsion gives a quadratic spin correction that enters the effective FLRW background equations with negative sign, so the torsion sector acts as an effective fluid with ρtor=-ρs, ptor=-ρs and stiff equation of state wtor=1.

“In Einstein-Cartan theory, algebraically eliminating torsion gives a quadratic spin correction.With the conventions used here, that correction enters the effective FLRW background equations with negative sign.I denote its magnitude by ρ s > 0 and write the torsion sector as an effective fluid, ρ tor ≡ -ρ s , p tor ≡ -ρ s ,”

In ECSK theory, torsion is sourced algebraically by the spin current and does not propagate; for a Dirac field it is fixed locally by the axial spin current.

“The coupling of spin to torsion is described by the Einstein-Cartan-Sciama-Kibble action, where the affine connection has an antisymmetric part and the spin current sources torsion [11,12].”

In EC theory, the intrinsic spin of fermions sources spacetime torsion, which at very high densities acts like a negative stiff component and can support a nonsingular bounce in homogeneous EC models without introducing new propagating degrees of freedom beyond GR plus matter.

“In EC gravity the intrinsic spin of fermions sources spacetime torsion, which at very high densities acts like a negative stiff component [11][12][13].This purely geometric effect can, in homogeneous EC models, support a nonsingular bounce without introducing new propagating degrees of freedom beyond GR plus matter.”