Vector stability in quadratic metric-affine theories

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.

23 pages, no figures, no tables. Some parts have been extended, rewritten and clarified. Version accepted for publication in JCAP

References in corpus (7)

• The Confrontation between General Relativity and Experiment
• Instability of anisotropic cosmological solutions supported by vector fields
• Dark Matter from R^2-gravity
• Generalized multi-Proca fields
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
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• Einstein-Proca theory from the Einstein-Cartan formulation
• Stability of Poincaré gauge theory with cubic order invariants
• A diffeomorphism invariant family of metric-affine actions for loop cosmologies
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Stability in Cubic Metric-Affine Gravity
• On parity-odd sector in metric-affine theories
• Friedmann cosmology with hyperfluids
• Gravitational waves in Cubic Metric-Affine Gravity