Metric-Affine Gauge Theories of Gravity

Metric-affine gauge theories of gravity generalise Einstein’s formulation by treating the spacetime metric and affine connection as independent fields. Drawing on the gauge principle applied to the general linear or affine group, these frameworks introduce curvature, torsion and non-metricity as dynamical quantities. The affine connection need not preserve metric compatibility, and its antisymmetric part gives rise to torsion, while deviations from covariant metricity produce non-metricity. Special cases such as the Einstein–Cartan theory, the Palatini formulation, teleparallel gravity and symmetric teleparallel models emerge as distinct realisations within this unified language. Metric-affine theories extend the reach of general relativity towards high-energy regimes, offering novel approaches to cosmic inflation, dark matter generation and singularity resolution. Ensuring theoretical consistency demands careful control of unphysical ghost modes via projective invariance and the appropriate coupling to matter currents characterised by hypermomentum.

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Metric-Affine Gauge Theories of Gravity publication trend

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Technical terms

Affine connection: A geometric object defining parallel transport and covariant differentiation, specifying how vectors change over spacetime independently of the metric.

Torsion: The antisymmetric part of the affine connection, representing a twisting of spacetime that couples naturally to intrinsic spin.

Non-metricity: A measure of the failure of the connection to preserve the metric under parallel transport, introducing novel gravitational interactions.

Projective invariance: A symmetry under reparametrisations of affine geodesics that removes unphysical scalar degrees of freedom from the connection.

Hypermomentum: A generalised source term combining spin, dilation and shear charges of matter that couples to affine geometric structures.

Palatini formalism: A variational approach in which metric and connection are varied independently, leading to extended gravitational dynamics beyond the purely metric variation.

References

1. Stability of non-degenerate Ricci-type Palatini theories. Journal of Cosmology and Astroparticle Physics (2023).
2. On the renormalization of Poincaré gauge theories. Journal of High Energy Physics (2024).
3. Coupling metric-affine gravity to the standard model and dark matter fermions. Physical Review D (2023).
4. Motion of test particles in spacetimes with torsion and nonmetricity. Physics Letters B (2024).
5. Spacetimes with vector distortion: Inflation from generalised Weyl geometry. Physics Letters B (2016).
6. New class of ghost- and tachyon-free metric affine gravities. Physical Review D (2020).