On the Reconstruction of the Scalar Mode of GW170817 in Scalar-Tensor Gravity Theory

In general metric theory of gravity, a gravitational wave is allowed to have up to six polarizations: two scalar and two vector modes in addition to tensor modes. In case the number of laser-interferometric gravitational wave telescopes is larger than the number of polarizations of a gravitational wave, all the polarizations can be individually reconstructed. Since it depends on theories of gravity which polarizations the gravitational waves have, the investigation of polarizations is important for the test of theories of gravity. In order to test the scalar–tensor gravity theory, one of important alternative theories of gravity, the scalar mode of GW170817 observed by LIGO Livingstone, Hanford and Virgo is reconstructed without prior information about any tensor–scalar gravity theories. The upper limit of the scalar mode in term of the band-limited root-sum-square of the amplitude is $$ with the time window of 2 s] and frequency window of ≈60–120 Hz]. It is also studied how much the tensor modes are leaked into the reconstructed scalar mode, and it is found that the reconstructed scalar mode contains roughly 30% of energy leaked from the tensor modes.