Irreducible decompositions in metric-affine gravity models

Abstract

The irreducible decomposition technique is applied to the study of classical models of metric-affine gravity (MAG). The dynamics of the gravitational field is described by a 12-parameter Lagrangian encompassing a Hilbert-Einstein term, torsion and nonmetricity square terms, and one quadratic curvature piece that is built up from Weyl's segmental curvature. Matter is represented by a hyperfluid, a continuous medium the elements of which possess classical momentum and hypermomentum. With the help of irreducible decompositions, we are able to express torsion and traceless nonmetricity explicitly in terms of the spin and the shear current of the hyperfluid. Thereby the field equations reduce to an effective Einstein theory describing a metric coupled to the Weyl 1-form (a Proca-type vector field) and to a spin fluid. We demonstrate that a triplet of torsion and nonmetricity 1-forms describes the general and unique vacuum solution of the field equations of MAG. Finally, we study homogeneous cosmologies with an hyperfluid. We find that the hypermomentum affects significantly the cosmological evolution at very early stages. However, unlike spin, shear does not prevent the formation of a cosmological singularity.

arXiv comment27 pages, RevTex

References in corpus (2)

• On the Gauge Aspects of Gravity
• Non-Riemannian Gravitational Interactions

Cited by in corpus (7)

• Cosmological Hyperfluids, Torsion and Non-metricity
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Cosmology of Quadratic Metric-Affine Gravity
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
• Quadratic Metric-Affine Gravity: Solving for the Affine-Connection
• Multipole solutions in metric--affine gravity
• General Einstein-Cartan quadratic gravity with derivative couplings