Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

Abstract

We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian that is quadratic in the field-strengths of the torsion and non-metricity vector traces. The theory result to be equivalent, on-shell, to a Vector-Tensor theory. We also discuss the sub-cases in which the contribution to the Lagrangian quadratic in the field-strengths of the torsion and non-metricity vectors just exhibits one of the aforementioned quadratic terms. We then report on implications of our findings in the context of $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity.

28 pages

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Cited by in corpus (9)

• Transit cosmological models in Myrzakulov F(R,T) gravity theory
• Einstein-Proca theory from the Einstein-Cartan formulation
• Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_m)$ gravity
• Metric-Affine Myrzakulov Gravity Theories: Models, Applications and Theoretical Developments
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in $f(Q)$ cosmology
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• Algebraic classification of the gravitational field in general metric-affine geometries
• On the dilation current in metric-affine gravity