Uncovering gravitational wave signatures of modified theories of gravity and exotic matter

Abstract

The observation of the first gravitational-wave (GW) event almost a decade ago opened a new promising window to our scientific endeavours in understanding the deepest mysteries of our Universe and its history. Using the foundations of general relativity (GR), we are now in the position of being able to model coalescence and merger of binary black holes and neutron stars, and understand how their modelled data fit within the manifold of our GW observations. A key ingredient in source modelling of binary systems is numerical relativity (NR), allowing us to resolve the merger regime and forming the foundation of this thesis. Despite the success of GR, many proposals of modified theories gravity and exotic compact objects have been put forward to address experimental data, theoretical inconsistencies of the theory of general relativity, and merely human curiosity of `what if?'. In the pursuit of addressing all of the open questions, we now find ourselves presented with an elaborate list of possible extensions to GR and the Standard Model of particle physics. Whilst we have not found any modification to gravity to be statistically preferred, with the rise of future GW detectors and increased number of events, we may be in position to even further constrain and test our theoretical proposals. However, in order to achieve this, we require accurate modelling of the phenomena we wish to study and understand its implications for GW observations. The goal of this thesis is to pave the path towards achieving this goal, by bringing together numerical relativity and GW analysis for certain modified theories of gravity and classes of exotic compact objects. We assume that the reader has some introductory knowledge about the theory of general relativity, numerical and statistical methods. However, we do review the key theoretical points and tools that have facilitated our studies. We start our discussion with the numerical study of binary black holes in Einstein-scalar-Gauss-Bonnet (EsGB) theory of gravity in the decoupling limit. An interesting feature of this theory is that black holes can posses scalar hair and the resulting gravitational-wave signals -- scalar polarisation. By focusing on the ringdown and modelling the scalar content of the theory, we forecast the ability of present and future GW detectors to measure it. We find that the ringdown scalar polarisation is undetectable with the current GW detectors, but that scalar ringdown of a limited number of binary configurations could be in principle measured with the design sensitivity of the next generation detectors. We next move to the discussion of a specific class of exotic compact objects -- boson stars (BSs). We first devise the numerical methods required to construct these objects as single spacetimes in spherical symmetry in GR. We then extend their study to massless and massive scalar-tensor (ST) theories of gravity. We perform a systematic study of the whole parameter space and study their stability. Overall, we find that similar to neutron stars, boson stars in ST theory can undergo spontaneous scalarisation, which may result in smoking-gun effects for future observations. However, BSs turn out to be less susceptible to scalarisation than neutron stars. By focusing on GR and moving away from the study of single boson-star spacetimes, we then consider them in the binary context. By focusing on head-on collisions, we devise a suitable method for constructing initial data for boson-star binaries of arbitrary mass ratio, allowing us to circumvent spurious and unphysical effects that arise from methods commonly employed in the literature. We explore the parameter space of head-on boson-star collisions and find that in certain regimes their GW signals exhibit conspicuous features of tidal deformation, posing a direct way of differentiating them from black holes. Finally, we apply our numerical infrastructure to inspiralling quasi-circular boson-star systems. We construct for the first time high-precision numerical relativity waveforms that we make publicly available. Further, we use our numerically simulated signals as injections into detector noise and assess the ability of standard binary black hole and neutron star waveform approximants to recover them. We find strong biases in the parameter estimation and show that even with the sensitivity of present GW detectors, certain binary boson-star systems, if present in the detector band, are likely to leave non-Gaussian residuals, signalling the presence of `new' physics. Given applications of gravitational wave analysis to numerical relativity presented in this thesis, we also include a brief guide on how to prepare numerical relativity waveforms as injections into detector noise. Our tools and methods may be applied to any theory of gravity and/or exotic compact objects, as long as one is able to model their resulting GW signals.