Torsionbased

Torsionbased refers to theories and geometrical frameworks in which torsion is the central dynamical quantity, rather than curvature, in the description of spacetime or other geometric spaces. In differential geometry, torsion is the antisymmetric part of the affine connection, T^λ_{ μν} = Γ^λ_{ μν} − Γ^λ_{ νμ}. When torsion is allowed to be nonzero, the underlying geometry is typically described as Riemann-Cartan or metric-affine.

Historically, Cartan introduced torsion as a generalization of Riemannian geometry. In Einstein–Cartan theory, torsion is sourced algebraically by the spin density of matter, yielding corrections to gravity that become relevant at extremely high densities, while in vacuum torsion does not propagate.

In broader torsionbased theories, torsion can be dynamical and propagate, appearing in actions that include torsion or contorsion terms. Examples include Poincaré gauge theory and certain metric-affine gravities. Teleparallel gravity is often framed as torsion-based because gravity is described by torsion with vanishing curvature, though definitions vary by formulation.

Applications of torsionbased frameworks span cosmology, quantum gravity, and particle physics. Spinor fields couple naturally to torsion, which can induce four-fermion interactions, and early-universe dynamics may differ from curvature-based models. Observational constraints on torsion are model-dependent and generally weaker than those on curvature, but ongoing work seeks possible torsion-induced signatures in high-density regimes or precise gravitational tests.

The term 'torsionbased' is not universally standardized but is used to classify approaches where torsion plays the defining role in the geometry or dynamics.