Torsion Gravity and Cosmological Theories

Torsion gravity encompasses a class of theories in which the geometry of spacetime is endowed not only with curvature but also with torsion, a tensorial quantity that represents the antisymmetric part of the affine connection. In its simplest realisation, the Einstein–Cartan framework couples this torsion to the intrinsic spin of matter fields, thereby extending general relativity without introducing extra dynamical degrees of freedom beyond those carried by spin and the metric. Such theories predict novel features in both astrophysical and cosmological settings. On cosmological scales, torsion may affect the early-universe dynamics through bounce scenarios that replace the classical singularity, generate repulsive interactions at high densities and offer an alternative to scalar-driven inflation. In homogeneous and isotropic models, torsion can modify the Friedmann and Raychaudhuri equations, mimicking spatial curvature or a cosmological constant, and thereby influence structure formation, primordial element abundances and late-time acceleration. Beyond cosmology, torsion also leaves imprints at the level of post-Newtonian dynamics, altering spin precession, gravitational radiation and multi-body motion. Experimental and observational constraints on torsion arise from tests of gravity in the solar system, neutron-spin experiments and astrophysical surveys, establishing stringent upper bounds on torsion’s magnitude while leaving open the possibility of subtle effects in extreme regimes.

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Torsion Gravity and Cosmological Theories publication trend

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Technical terms

Torsion: The antisymmetric component of an affine connection that quantifies the failure of parallelograms to close in a manifold, representing a “twist” in spacetime geometry.

Einstein–Cartan theory: A classical extension of general relativity in which spacetime torsion is sourced by the intrinsic spin density of matter, leading to non-Riemannian geometric effects without propagating torsion waves.

Friedmann equations: The set of ordinary differential equations governing the scale factor of a homogeneous and isotropic universe, derived from the gravitational field equations under the cosmological principle.

Weyssenhoff fluid: An idealised macroscopic medium endowed with intrinsic spin, used to model the collective spin effects of fermionic matter in Einstein–Cartan cosmology.

Post-Newtonian approximation: A perturbative expansion of the gravitational field equations in orders of (v/c), used to calculate corrections to Newtonian gravity in the weak-field, slow-motion regime.

References

1. First post-Newtonian N-body problem in Einstein–Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals. European Physical Journal C (2023).
2. Signature of Einstein-Cartan theory. Physics Letters B (2024).
3. Cosmology with torsion: An alternative to cosmic inflation. Physics Letters B (2010).
4. Friedmann-like universes with torsion. European Physical Journal C (2019).