Gravitational waves in Einstein–Cartan theory: On the effects of dark matter spin tensor

Abstract

This article studies the effects of an arbitrary dark matter spin tensor on the propagation of gravitational wave amplitude in the context of Einstein–Cartan theory. We choose to work with an arbitrary spin tensor because, given our ignorance of the nature of dark matter, it is sensible not to make further hypotheses on its spin and not to assume any particular model for its spin tensor (or its vanishing). The analysis focuses on a “weak-torsion regime”, such that gravitational wave emission, at leading and subleading orders, does not deviate from standard General Relativity. We show that, in principle, the background torsion induced by an eventual dark matter spin component could lead to an anomalous dampening or amplification of the gravitational wave amplitude, after going across a long cosmological distance. We assess the importance of this torsion-induced anomalous amplitude propagation for binary black hole mergers in a way as model-free as possible in Einstein–Cartan gravity. It is possible to prove that at its best, for realistic late-universe cosmological scenarios, the effect is tiny and falls below detection thresholds, even for near-future interferometers such as LISA. Therefore, detecting this effect may not be impossible, but it is still beyond our technological capabilities. As a model-independent result in the Einstein–Cartan context, it also implies that mergers are robust standard sirens without considering any potential dark-matter-induced torsional effects.