Vector stability in quadratic metric-affine theories
arXiv:2205.05674 · doi:10.1088/1475-7516/2022/09/044
Abstract
In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions the spin-1 modes associated to such vectors can propagate in a safe way, together with the graviton. This highly constrains the theory reducing the parameter space of the quadratic curvature part from 16 to 5 parameters. We also study the sub-case of Weyl-Cartan gravity, proving that the stability of the vector sector is only compatible with an Einstein-Proca theory for the Weyl vector.
arXiv comment23 pages, no figures, no tables. Some parts have been extended, rewritten and clarified. Version accepted for publication in JCAP
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