Scalar and tensor gravitational waves

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.

Comparing the luminosity distance for gravitational waves and electromagnetic signals in a simple model of quadratic gravity

“…(see also [8][9][10][11]13,14] for a detailed discussion of how the GW amplitude h is related to the GW luminosity distance).…”

“…In such a context it is important to note that, by comparing the propagation of GW signals received from a given source and the propagation of other ultra-relativistic signals emitted by the same source, we have also the possibility of testing alternative theories of gravity on a cosmic scale of distance, as recently stressed and discussed in [8][9][10][11] (see also [12][13][14][15]).…”

“…The model is also known as "Starobinsky gravity" [20], and can be regarded as a truncated higher-curvature expansion of the gravitational action. Also, it corresponds to a simple type of f (R)-gravity and can be related to the largest class of Horndeski theories, widely used to test gravity through modified GW propagation (see in particular [21] and [11,13,14]). It was shown [22] that such a model can fit the Hubble diagram of Supernovae, consistently with other recent cosmic data, even in the absence of an explicit dark-energy contribution.…”

Stability and phase transition of rotating Kaluza–Klein black holes

“…Therefore, the fingerprint of scalar fields on gravitational waves could be detected by employing future gravitational wave detectors. However, the interactions of scalar and tensor waves generally depend on the scalar propagation speed such that the interactions are negligible whether the scalar waves are luminal or quasi-luminal [29].…”

Gravitational-wave cosmological distances in scalar-tensor theories of gravity

“…Recently, various scenarios have been analyzed[55][56][57][58] where, at the price of tunings, tensor and scalar propagate with the same speed. We do not consider this case in this work.…”