Metric-Affine Vector-Tensor correspondence and implications in F(R, T, Q, T, D) gravity

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 contri-bution, 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 results 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 cosmological aspects of the general quadratic theory in the presence of a perfect cosmological hyperfluid and on implications of our findings in the context of F(R, T, Q, T, D) gravity.(c) 2022 Elsevier B.V. All rights reserved.