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Item Studies in alternative theories of gravity and advanced data analysis(Montana State University - Bozeman, College of Letters & Science, 2024) Gupta, Toral; Chairperson, Graduate Committee: Neil J. Cornish; This is a manuscript style paper that includes co-authored chapters.The field of gravitational wave astronomy is generating groundbreaking findings, yielding unique insights on some of the most extraordinary phenomena in the universe and providing invaluable information on testing the principles of general relativity. All gravitational wave signals detected so far appear to come from compact binaries - black holes and neutron stars. We use information from these sources to probe strong fields of gravity and to constrain modified theories of gravity. However, solely relying on template- based searches for known astrophysical sources biases our gravitational wave signal search towards well-modeled systems, potentially overlooking unpredicted sources with limited theoretical models, hindering the extraction of new physics. Further work in this thesis focuses on building improved signal and noise models to enhance our capability of detecting gravitational signals of all within and beyond the constraints of theoretical predictions. This includes introduction of new basis functions with added modifications to develop a signal-agnostic waveform reconstruction model using Bayesian inference. Additionally, this study discusses improvements in the speed and performance of the BayesWave trans-dimensional Bayesian spectral estimation algorithm, which includes implementing a low-latency analysis and various enhancements to the algorithm itself. In essence, this study is centered on developing a comprehensive understanding, both theoretical and observational, of astrophysical objects along with the spacetime that governs their dynamics.Item Exploring the low-frequency gravitational-wave universe with pulsar timing arrays(Montana State University - Bozeman, College of Letters & Science, 2022) Becsy, Bence; Chairperson, Graduate Committee: Neil J. Cornish; This is a manuscript style paper that includes co-authored chapters.Pulsar timing arrays monitor millisecond pulsars to detect gravitational waves with nanohertz frequencies. They provide valuable information about various astophysical processes inaccessible to electromagnetic observations. In particular, they could shed light on unsolved problems related to the formation and evolution of supermassive black holes. We present several new methods which will help us fully realize the detection potential of pulsar timing arrays. We explore how the large collection of supermassive black hole binaries in the Universe can appear as a stochastic gravitational wave background, and how it might also result in a few individually detectable binaries. We describe a new method to efficiently search for such individual binaries, and also how we can detect multiple binaries in the presence of the confusion noise from the stochastic background. Finally, we introduce a new approach to search for generic gravitational-wave bursts, which enables us to hunt for unexpected new types of sources on the nanohertz gravitational-wave sky.Item Eccentric gravitational waves: modeling and data analysis implications(Montana State University - Bozeman, College of Letters & Science, 2020) Moore, Blake Carroll; Chairperson, Graduate Committee: Nicolas Yunes and Neil J. Cornish (co-chair); Travis Robson, Nicholas Loutrel and Nicolas Yunes were co-authors of the article, 'A Fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicholas Loutrel was a co-author of the article, 'A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Data analysis implications of moderately eccentric gravitational waves' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.; Nicolas Yunes was a co-author of the article, 'Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.The ground based advanced Laser Interferometer Gravitational wave Observatory (LIGO) has now made numerous detections of compact objects, ushering in an era of gravitational wave astronomy. Soon the Laser Interferometer Space Antenna (LISA) will become operational and allow for even more detections of gravitational waves. With these detections we are able to characterize the physical properties of the sources - the nature of the orbit, the parameters of the individual compact object, and the parameters of the final merged object. Beyond these source measurements, gravitational waves have proven an important test bed for validating General Relativity, as well as testing theoretical astrophysical formation scenarios of these compact binaries. In order to reach these ends, we require accurate and efficient models for the gravitational waves as seen in the detector. While current detections by ground based detectors are consistent with compact binaries in quasi-circular orbits, there are formation scenarios which suggest that some small number of detectable events will be from compact objects in eccentric orbits, and certainly a healthy number of sources detectable by LISA will be in eccentric orbits. We have derived, validated, and explored the data analysis properties of a waveform model for compact objects in eccentric orbits. In the derivation of the waveform we have employed a truncated sum of harmonics, the stationary phase approximation, and a bivariate expansion in eccentricity and orbital velocity. To explore the data analysis implications of this model we have implemented Markov Chain Monte Carlo algorithms to produce the posterior distributions on the waveform parameters. We find that our model is highly accurate for the inspiral phase of compact objects in orbits with eccentricity as high as 0.8, and very computationally efficient - taking only 90ms to evaluate on average. System parameters are best measured when the source eccentricity is about 0.4, sometimes providing two orders of magnitude better measurement than its quasi-circular counterpart, and eccentric signals can provide more stringent constraints on alternative theories of gravity.