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#### Tests of General Relativity with Gravitational-Wave Observations using a Flexible--Theory-Independent Method

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##### Citation

Mehta, A. K., Buonanno, A., Cotesta, R., Ghosh, A., Sennett, N., & Steinhoff, J. (in preparation). Tests of General Relativity with Gravitational-Wave Observations using a Flexible--Theory-Independent Method.

Cite as: https://hdl.handle.net/21.11116/0000-000A-3198-3

##### Abstract

We perform tests of General Relativity (GR) with gravitational waves (GWs)

from the inspiral stage of compact binaries using a theory-independent

framework, which adds generic phase corrections to each multipole of a GR

waveform model in frequency domain. This method has been demonstrated on

LIGO-Virgo observations to provide stringent constraints on post-Newtonian

predictions of the inspiral and to assess systematic biases that may arise in

such parameterized tests. Here, we detail the anatomy of our framework for

aligned-spin waveform models. We explore the effects of higher modes in the

underlying signal on tests of GR through analyses of two unequal-mass,

simulated binary signals similar to GW190412 and GW190814. We show that the

inclusion of higher modes improves both the precision and the accuracy of the

measurement of the deviation parameters. Our testing framework also allows us

to vary the underlying baseline GR waveform model and the frequency at which

the non-GR inspiral corrections are tapered off. We find that to optimize the

GR test of high-mass binaries, comprehensive studies would need to be done to

determine the best choice of the tapering frequency as a function of the

binary's properties. We also carry out an analysis on the binary neutron-star

event GW170817 to set bounds on the coupling constant $\alpha_0$ of

Jordan-Fierz-Brans-Dicke gravity. We take two plausible approaches; in the

first \emph{theory-agnostic} approach we find a bound $\alpha_0 \lesssim

2\times 10^{-1}$ from measuring the dipole-radiation for different neutron-star

equations of state, while in the second \emph{theory-specific} approach we

obtain $\alpha_0 \lesssim 4\times 10^{-1}$, both at $68\%$ credible level.

These differences arise mainly due to different statistical hypotheses used for

the analysis.

from the inspiral stage of compact binaries using a theory-independent

framework, which adds generic phase corrections to each multipole of a GR

waveform model in frequency domain. This method has been demonstrated on

LIGO-Virgo observations to provide stringent constraints on post-Newtonian

predictions of the inspiral and to assess systematic biases that may arise in

such parameterized tests. Here, we detail the anatomy of our framework for

aligned-spin waveform models. We explore the effects of higher modes in the

underlying signal on tests of GR through analyses of two unequal-mass,

simulated binary signals similar to GW190412 and GW190814. We show that the

inclusion of higher modes improves both the precision and the accuracy of the

measurement of the deviation parameters. Our testing framework also allows us

to vary the underlying baseline GR waveform model and the frequency at which

the non-GR inspiral corrections are tapered off. We find that to optimize the

GR test of high-mass binaries, comprehensive studies would need to be done to

determine the best choice of the tapering frequency as a function of the

binary's properties. We also carry out an analysis on the binary neutron-star

event GW170817 to set bounds on the coupling constant $\alpha_0$ of

Jordan-Fierz-Brans-Dicke gravity. We take two plausible approaches; in the

first \emph{theory-agnostic} approach we find a bound $\alpha_0 \lesssim

2\times 10^{-1}$ from measuring the dipole-radiation for different neutron-star

equations of state, while in the second \emph{theory-specific} approach we

obtain $\alpha_0 \lesssim 4\times 10^{-1}$, both at $68\%$ credible level.

These differences arise mainly due to different statistical hypotheses used for

the analysis.