Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1

Abstract

The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low-and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be m g ≤ 4.7 × 10 −23 eV=c 2 (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.

Spherically symmetric solutions in torsion bigravity

“…We can use the inverse of these equations (see Eqs. (7.13)) to express V 2 and Y 2 in terms of V m0(2) and V mk (2) . When expanding to second order our basic field equations E 1 -E 5 ,(5.17)-(5.21), we first get algebraic equations for F 2 and Λ 2 of the form…”

“…where the second-order source terms S m0 (2) and S mk (2) consist of terms bilinear in V 1 , Y 1 , F 1 , Λ 1 , together with additional contributions linear in the pressure P 2 (remembering that P is second-order, see section VII). We recall that P 2 is obtained by solving the matter equation…”

“…Let us explain it. We recall that the second-order variables F 2 and Λ 2 are expressed in terms of the second-order potentials V m0 (2) and V mk (2) via the equations…”

“…Here, the additional (nonlinear) terms N F 2 , N Λ 2 (which are bilinear in V 1 , Y 1 , F 1 , Λ 1 and their derivatives) do contain some 1/κ 2 factors, but all these factors have a special structure: each monomial containing a factor κ −2 simultaneously contains at least one power of Y 1 or of one of its derivatives. Similarly, the potentials V m0 (2) and V mk(2) satisfy the differential equations (8.4) where the source functions S m0 (2) and S mk (2) consist of terms bilinear in V 1 , Y 1 , F 1 , Λ 1 and their derivatives. Again the latter bilinear expressions S m0 (2) , S mk (2) do contain some 1/κ 2 factors, but the latter a priori dangerous (when κ → 0) terms have the same special structure as N F 2 , N Λ 2 .…”

“…General Relativity (GR), has, so far, been found to be in excellent accord with all gravitational observations and experiments. In particular, its foundational stone, the weak equivalence principle, has been recently confirmed at the 10 −14 level [1], while gravitational-wave observations have confirmed several basic dynamical predictions of GR [2,3]. [See, e.g., chapter 20 in Ref.…”