Condition for directly testing scalar modes of gravitational waves by four detectors

TL;DR

This paper proposes a method using four ground-based gravitational wave detectors to directly test for scalar polarization modes of gravitational waves by identifying specific sky locations where vector and tensor modes can be eliminated.

Contribution

It introduces a new condition based on a single equation on the celestial sphere that allows for the separation of scalar modes from vector and tensor modes in GW observations.

Findings

A specific sky location condition eliminates vector and tensor modes.

Adding LIGO-India enhances the test feasibility.

The method improves the potential for direct scalar mode detection.

Abstract

General metric theories in a four-dimensional spacetime allow at most six polarization states (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). If a sky location of a GW source with the electromagnetic counterpart satisfies a single equation that we propose in this paper, both the spin-1 modes and spin-2 ones can be eliminated from a certain combination of strain outputs at four ground-based GW interferometers (e.g. a network of aLIGO-Hanford, aLIGO-Livingston, Virgo and KAGRA), where this equation describes curves on the celestial sphere. This means that, if a GW source is found in the curve (or its neighborhood practically), a direct test of scalar (spin-0) modes separately from the other (vector and tensor) modes become possible in principle. The possibility of such a direct test is thus higher than an earlier expectation (Hagihara et al. PRD, 100, 064010, 2019), in which they argued that the vector modes could not be completely eliminated. We discuss also that adding the planned LIGO-India detector as a fifth detector will increase the feasibility of scalar polarization tests.