Analytic Modelling of Gravitational-Wave Source in General Relativity and Alternative Theories of Gravity

Abstract

The first direct detection of gravitational waves (GWs) by LIGO in 2015 opened up new avenues for probing and better understanding the strong-field dynamics of gravity. The continuous improvement in the sensitivity of LIGO, Virgo and now KAGRA along with the forthcoming next-generation detectors like the Einstein Telescope and LISA, will provide a wealth of GW signals to study strong-field dynamics, and to probe the nature of compact objects. Alternative gravitational theories generally predict dynamics different from GR, therefore, it is also expected that the observations of GWs will shed more light on these theories by constraining their parameters. In addition to the applications in usual parameter estimation to improve the constraints, the analytical modelling of waveform generation considered in our work can be used to build search pipelines for the specific beyond GR model considered here. The detection (searches and parameter estimation) of GWs is based on matching the data observed in the detectors against theoretically predicted waveforms. Hence, highly accurate analytical models are required to construct a bank of waveform templates. The analytical waveform template banks used by LIGO are based on the post-Newtonian (PN) formalism for inspiral and on numerical relativity (NR) for merger and ringdown, or resummation methods such as the effective-one-body (EOB) formalism to describe the complete dynamics. In this thesis, we discuss the construction of analytical waveform models within the EOB formalism for a specific alternative theory of gravity the so-called massless scalar-tensor theory. More specifically, we describe the map of the dynamics of a binary system in scalar-tensor theory into the EOB formalism by building upon the PN expanded Lagrangian of the two-body problem at 3PN order. We discuss the generalization of the 2PN EOB Hamiltonian to 3PN order for the conservative part of the dynamics and then compute the scalar-tensor corrections to EOB potentials for generic orbits. We also compute the corrections in the EOB Hamiltonian due to tidal effects at 3PN order for circular orbits. Following this, we describe the derivation of the angular momentum flux in the scalar-tensor theory for both the scalar part and the tensorial part up to 1PN and 1.5PN order, respectively. We then use these results along with the energy flux to compute generic orbit radiation reaction effects in the EOB formalism up to 1PN order. Finally, we use the 3PN conservative dynamics results in the EOB formalism to derive the scattering angle in the scalar-tensor theories which can be used in future as a check against the scattering angle computed using scattering amplitude techniques. Finally, we implement up to 3PN conservative dynamics results in the EOB based waveform model TEOBResumS. Additionally, we investigate the improvement in the inference of the properties of neutron stars using the information of the observation of electromagnetic counterparts of the GW signal GW170817 and improved fits of the threshold mass. The application of the improved fits to the GW170817 signal implies that a significant part of the parameter space is not supported by the observation of the EM counterpart, implying improved constraints on the neutron star radii and hence the equation-of-state.