Testing General Relativity With Gravitational Waves From Compact Binaries

Since the first detection of the gravitational wave (GW) event GW150914 by the LIGO and Virgo Collaborations in 2015, over 90 transients have been observed. In addition to the typical binary black hole (BBH) events demonstrated by GW150914, there are other types of events, namely binary neutron star mergers (e.g., GW170817) and neutron star-black hole binary events (e.g., GW200105, GW200115), which provide additional perspectives for the examination of gravitational theories. Furthermore, using X-rays, the Neutron Star Interior Composition Explorer has enabled the measurement of the mass and radius of an isolated neutron star, which means that testing gravity in the strong field regime could now be applied to not only black hole dynamics but also to neutron stars and black hole-neutron star interactions. This thesis focuses on analyzing the profiles of neutron stars analytically and studying tests of gravity using GW events associated with neutron stars and black holes.

Before employing neutron stars to test General Relativity (GR), we study analytical properties of these astrophysical objects. Universal relations have been discovered that are insensitive to the equation of state (EoS) of neutron stars, and they have important applications for probing fundamental physics, such as nuclear and gravitational physics. However, there is a lack of analytic works on universal relations for realistic neutron stars, which hinders a better understanding of universality. In this thesis, we focus on the universal relations between the compactness (C), the moment of inertia (I), and the tidal deformability (related to the Love number), and derive analytic, approximate I-Love-C relations. In order to construct slowly-rotating/tidally-deformed neutron star solutions, we first derive an analytic model of the static and isolated neutron star interior. We introduce an improved analytic model based on the Tolman VII solution that includes an additional parameter to have a better match with density profiles obtained numerically. The improvement is by a factor of 2∼5 and this additional parameter can also be fitted in an EoS-insensitive way in terms of the stellar mass, radius, and central density. Using this improved analytic profile, we solve for the slowly-rotating and tidally deformed neutron star profile through perturbation theory. Our results mathematically demonstrate the O(10%) EoS variation in the I-C and Love-C relations and the O(1%) variation in the I-Love relation that have previously been found numerically.

Next, we explore the prospects of probing potential non-GR effects in the propagation of GWs emitted by binary neutron star (BNS) mergers. Previous tests of this kind relied on an electromagnetic (EM) counterpart to compare with the GW signals. However, we propose an alternative approach that uses BNS mergers without EM counterparts to investigate modified GW propagation through the tidal effects. This method measures the redshift with the tidal Love number, which is linked to the intrinsic masses of the neutron stars. By combining the redshifted mass measurement with the tidal information, we can break the degeneracy between the redshift and the intrinsic mass to extract the former. We consider multi-band observations using both ground-based and space-based interferometers over a 3-year observation period. Our results show that such multi-band observations with tidal information can more stringently constrain a parametric non-Einsteinian deviation in the luminosity distance (arising from modified friction in the GW evolution) compared to relying solely on EM counterparts, by a factor of a few. We also map the constraint on the GW propagation parameter to bounds on parameters in various beyond-GR gravity theories.

In our next project, we investigate how neutron star-black hole (NSBH) GW events set a more stringent bound on a particular modified theory of gravity, Einstein-dilaton-Gauss-Bonnet (EdGB) gravity. We show that the leading order correction to the evolution of the GW phase, originating from the scalar dipole radiation, is inversely proportional to the fourth power of the total mass of the system. As a result, smaller total mass systems would give a more significant contribution to this correction. Moreover, the scalar dipole radiation scales with the square of the difference in the scalar charges for two bodies in a binary. Thus, (stellar-mass) NSBH binary systems are well-suited to impose further constraints on EdGB gravity. Our analysis yields a stronger bound on the EdGB parameter αGB than that obtained by combining selected BBH systems from the GWTC-1 and GWTC-2 catalogs. Furthermore, we improve upon this analysis by including higher order corrections up to the second post-Newtonian order in phase evolution, and we find that there is roughly a 10% improvement on the bounds.

In the final chapter, we present our ongoing work on speeding up the parameter estimation for beyond-GR parameter inference for BBH signals using neural networks. Standard methods used to estimate their source parameters employ computationally expensive Bayesian inference approaches (e.g. the Bayesian inference performed in the project mentioned in the previous paragraph takes ∼ a day to finish). Here, we intend to use conditional variational autoencoder to perform the task, and we have succeeded in four-parameter estimation for BBH GW signals. The addition of non-GR modification to the training samples remains in progress.