Vector stability in quadratic metric-affine theories

TL;DR

This paper investigates the stability of vector modes in quadratic metric-affine gravity theories, identifying conditions for safe propagation and reducing parameter space, with implications for Weyl-Cartan gravity.

Contribution

It analyzes vector stability in quadratic metric-affine theories, constrains parameters for safe propagation, and links Weyl vector stability to Einstein-Proca theory.

Findings

Stability conditions reduce quadratic curvature parameters from 16 to 5.

Weyl vector stability is compatible only with Einstein-Proca theory.

Identifies parameter constraints ensuring safe vector mode propagation.

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.