Testing the fidelity of waveform reconstruction for gravitational wave transients using minimal assumptions

On the 14th of September 2015, the first direct detection of gravitational waves (GWs) was made by the LIGO and Virgo collaborations. This discovery opened a new era in astronomy and physics, allowing us to observe the Universe under a different light. Since then, hundreds of detections have been made in the years, and many more are expected to come. These observations can now be used to test our understanding of the Universe and gain a deeper understanding binding astrophysics, cosmology and General Relativity (GR). Among all the methodologies to study GW events, burst searches play a central role in the detection of GWs, as they are designed to detect a wide variety of signals without relying on a specific waveform model. Such searches play a crucial role, since they can either detect signals that are not modeled, or be sensitive to deviations from the theoretical predictions of GR. Among all the burst search pipelines, coherent WaveBurst (cWB) is one of the most successful and widely used, as it has been able to detect dozens of signals with high significance.While modeled searches can only reconstruct signals as predicted by GR, burst searches can, in principle, detect deviations from theoretical models, capture hard-to-model distortions of the waveform due to effects like precession or eccentricity, or even help detecting exotic signals like post-merger echoes or cosmic strings—ultimately testing the predictions of GR and looking for new physics. In such a context, the fidelity of the reconstruction of the waveform plays a crucial role, as only with a good reconstruction of the signal we can perform meaningful tests of the underlying physics. For this reason, the focus on the thesis is the investigation of the fidelity of the waveform reconstruction inside the burst framework, and in particular with the pythonized version of cWB: py coherent WaveBurst (pycWB). The first part of the thesis (Chapters 1-4) is dedicated to the introduction of the theoretical background and the state of the art of burst searches, with a particular focus on cWB. Chapter 1 introduces the theory of GWs in the context of GR, and the history of their detection. Together with this brief introduction, some of the known sources of GWs are introduced. Particular emphasis is put on the sources of GW transients, the main target of burst searches. Chapter 2 gives a short introduction to the detection of GWs, describing the detectors and the data analysis techniques used in the field. Chapter 3 is dedicated to the description of the cWB pipeline, with a particular focus on the analysis workflow, the main algorithms and the statistical approach to the detection of candidate signals. Together with the algorithm, its pythonized version (pycWB) is described. Chapter 4 introduces the principle of Maximum Entropy applied to the estimate of Power Spectral Density of some observed process. This advanced technique displays several advantages with respect to standard ones, providing a low-bias high-resolution estimate of the power spectral density. This is the last theoretical bit needed to understand the results of the thesis. The second part of the thesis (Chapters 5-8) is dedicated to the investigation of the fidelity of the waveform reconstruction in the burst framework. The fidelity is assessed by investigating both the bias (Chapters 5 and 6) and the variance (Chapter 7) of the reconstruction. In order, we investigate: the accuracy of the waveform reconstruction (Chapter 5 and 6), the construction of confidence belts around the waveform (Chapter 7), and the construction of a new test statistic based on the concept of the Network Covariance Matrix. Chapter 5 is dedicated to the investigation of the pre-processing step of the pipeline. We show that two improvements in the pipeline can be achieved. The first regards the tuning of the wavelet transform used in pycWB. We show that the current time-frequency representation is sub-optimal, and that an improved version can be obtained by easily changing the parameters of the transform. The second improvement regards changing the whitening method from the standard one to the Maximum Entropy method described in Chapter 4. We build a new whitening algorithm and compare the pre-processing of the data with the old version of the pipeline and the new one. Chapter 6 investigates how the improvement of the pipeline made in Chapter 5 affects the accuracy of the waveform reconstruction. Here, we focus on different types of signals, and show that the modification of the wavelet transform leads to a small but detectable improvement in the accuracy of the reconstruction for different signal morphologies. Chapter 7 is again partly theoretical. The standard cWB and pycWB estimate for the waveform only produce point estimates, i.e. a denoised estimate of the signal over time, with no uncertainty over the process. To address this limitation, we introduce a bootstrap method to estimate the uncertainty of the waveform reconstruction and show how it can be used to construct confidence intervals in the context of pycWB, reporting some case examples. Chapter 8 takes the improvements made in Chapters 5 and 6 and, using the bootstrap method, and explores a novel method to use burst-estimates to perform statistical inference. We exploit the bootstrap methodology to build a “Network Covariance Matrix”, a statistical tool that describes the variability of the reconstruction in a network of detectors, taking into account the correlation between the different detectors and different time samples of every detector. Considering the example of the GW250114 event, we show how this statistic can be used to build a powerful test statistic that can be used in three different cases, namely parameter estimation, model selection and hypothesis testing.