Effective Einstein theory from metric-affine gravity models via irreducible decompositions

Details Effective Einstein theory from metric-affine gravity models via irreducible decompositions Effective Einstein theory from metric-affine gravity models via irreducible decompositions

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrvd..56.7769o&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 56, Issue 12, 15 December 1997, pp.7769-7778

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37

Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity, Other Special Classical Field Theories, Exact Solutions

Scientific paper

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 a 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.

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