Abstract
With the historic detection of gravitational waves (GWs) by the LIGO and Virgo collaborations (LVC) in 2015, an era of GW astronomy began. Almost fifty binary merger events have been detected from the first two and a half observing runs of LVC. Ripples in the curvature of spacetime created by coalescing compact binaries allowed us to perform tests of gravity in strong and dynamical field regimes that were previously unexplored. Testing gravity in such a field regime is of particular importance to probe modified theories of gravity, which are viable modifications to general relativity (GR), motivated from both theoretical and observational aspects. This thesis considers both theory-agnostic and theory-specific approaches for testing a number of modified theories of gravity with GWs.
Theory-agnostic or model-independent tests have the advantage over theory-specific tests, as one can map the results of one particular test to several theories. Adopting parametrized post-Einsteinian formalism, we introduce generic deviations to the amplitude and phase of gravitational waveforms from those of GR. We derive analytic expressions of such deviations in a number of theories. We further perform numerical analyses with GW events GW150914 and GW151226 to achieve bounds on such deviations. Finally, we map such bounds to some modified theories of gravity to achieve constraints on those theories. A critical feature of our work is that we keep non-GR deviations in both phase and amplitude of the waveform while performing numerical analyses, while most works done previously focused on corrections to the GW phase only.
For theory-specific cases, we first consider higher-dimensional scenarios. One of the many avenues of modifying the four-dimensional theory of GR is to introduce extra dimensions. Such modifications are motivated by string theories in order to achieve a quantum theory of gravity. We study theories that contain extra dimensions compactified on circles. In particular, we compute modifications induced by compact extra dimensions to the binding energy of binaries and the luminosity of GWs generated by them. We compute the GW phase using such quantities and compare it with GW and binary pulsar observations. Such comparisons show inconsistency between the prediction of our model and the observations, which rules out the class of simple compactified higher-dimensional models.
Finally, we study GW memory effects, a set of strong-field GW phenomena yet to be detected. Such effects manifest as permanent changes in the GW strain and its time integrals after the passage of GWs. They are closely related to asymptotic symmetries of the spacetime and corresponding conserved charges. GW memory effects are well studied in GR but need to be carefully investigated in theories beyond GR. To do so, we consider Brans-Dicke theory which contains a massless scalar field nonminimally coupled to gravity. GWs in Brans-Dicke theory can have three polarizations— two tensor modes (which are present in GR) and one scalar or breathing mode. We study Brans-Dicke theory in Bondi-Sachs framework and derive asymptotically flat solutions, asymptotic symmetries, and associated fluxes of conserved charges. We find that the connection between symmetries and memory effects in Brans-Dicke theory is different from that of GR. In particular, the symmetries are the same as those of GR, but there are two memory effects associated with the non-GR breathing polarization not related to spacetime symmetries.
We further implement the connection between memory effects and fluxes of conserved charges to compute GW memories associated with tensor polarizations in Brans-Dicke theory. We derive memory effects generated by quasi-circular nonprecessing binaries and find that tensor memories in Brans-Dicke theory have two unique features. First, they depend on the sky angles differently from those of GR, which can potentially constrain Brans-Dicke theory with future space-based GW detectors. Second, in terms of binary's relative velocity, they start at a lower order than those of GR.
