Scalar and tensor gravitational waves

TL;DR

This paper investigates how scalar and tensor gravitational waves propagate and interact in certain dark energy models, revealing that scalar-tensor interactions are minimal if scalar waves travel at or near the speed of light.

Contribution

It provides a detailed analysis of scalar and tensor wave interactions in Horndeski theories, clarifying conditions under which scalar waves influence gravitational wave observations.

Findings

Scalar-tensor interactions depend on scalar wave speed.

Interactions are negligible if scalar waves are luminal or quasiluminal.

Sub-luminal scalar waves have suppressed interactions due to phase incoherence.

Abstract

In dark-energy models where a scalar field is nonminimally coupled to the spacetime geometry, gravitational waves are expected to be supplemented with a scalar mode. Such scalar waves may interact with the standard tensor waves, thereby affecting their observed amplitude and polarization. Understanding the role of scalar waves is thus essential in order to design reliable gravitational-wave probes of dark energy and gravity beyond general relativity. In this article, we thoroughly investigate the propagation of scalar and tensor waves in the subset of Horndeski theories in which tensor waves propagate at the speed of light. We work at linear order in scalar and metric perturbations, in the eikonal regime, and for arbitrary scalar and spacetime backgrounds. We diagonalize the system of equations of motion and identify the physical tensor mode, which differs from the metric perturbation. We find that interactions between scalar and tensor waves generally depend on the scalar propagation speed. If the scalar waves are luminal or quasiluminal, then interactions are negligible. In the subluminal case, scalar-tensor interactions are effectively suppressed due to the incoherence of the wave's phases.