Gravitational waves in Cubic Metric-Affine Gravity

TL;DR

This paper derives exact gravitational wave solutions with dynamical torsion and nonmetricity in cubic Metric-Affine Gravity, revealing a scalar polarization mode that extends beyond General Relativity's tensor modes.

Contribution

It introduces new exact pp-wave solutions in cubic MAG with dynamical torsion and nonmetricity, highlighting a novel scalar polarization mode in gravitational waves.

Findings

Discovered pp-wave solutions with dynamical torsion and nonmetricity.

Identified a scalar polarization mode in gravitational waves.

Provided phenomenological signatures beyond GR's tensor modes.

Abstract

We derive new exact gravitational wave solutions with dynamical torsion and nonmetricity tensors in the framework of cubic Metric-Affine Gravity (MAG). For this purpose, we consider the full algebraic classification of the gravitational field in general metric-affine geometries and impose a set of Type N conditions on the field strength tensors that implement the kinetics of torsion and nonmetricity in a particular cubic MAG model, recently considered to eliminate ghostly instabilities from the vector and axial sectors of the theory. The new solutions represent pp-waves characterised by a metric function that includes the dynamical contributions of the torsion and nonmetricity tensors provided by the field equations of the model. In particular, these quantities induce a scalar polarisation mode in the gravitational-wave spectrum, thus offering a distinctive phenomenological signature beyond the ordinary tensor polarisation modes of General Relativity.