Vector stability in quadratic metric-affine theories

Alejandro Jim\'enez-Cano; Francisco Jos\'e Maldonado Torralba

Vector stability in quadratic metric-affine theories

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arxiv 2205.05674 v2 pith:42B6KLAI submitted 2022-05-11 gr-qc hep-th

Vector stability in quadratic metric-affine theories

Alejandro Jim\'enez-Cano , Francisco Jos\'e Maldonado Torralba This is my paper

classification gr-qc hep-th

keywords vectorquadraticstabilitymetric-affinetheoryassociatedcompatibleconditions

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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.

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