Testing general relativity and cosmology with gravitational waves: polarizations, propagation speeds, and backgrounds

Schumacher, Kristen Elisabeth

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https://hdl.handle.net/2142/129467 Copy

Description

Title

Testing general relativity and cosmology with gravitational waves: polarizations, propagation speeds, and backgrounds

Author(s)

Schumacher, Kristen Elisabeth

Issue Date

2025-04-29

Director of Research (if dissertation) or Advisor (if thesis)

Yunes, Nicolás

Doctoral Committee Chair(s)

Witek, Helvi

Committee Member(s)

• Noronha-Hostler, Jacquelyn
• Shaffer, Eric

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• gravitational wave data analysis
• tests of general relativity
• gravitational wave polarizations
• gravitational wave background
• Einstein-æther theory
• modified theories of gravity
• Lorentz-violation
• cosmology
• standard sirens

Abstract

Gravitational waves have enabled innumerable tests of various aspects of physics and astronomy, both through their detection and non-detection. This dissertation focuses on two primary areas that gravitational waves have impacted: general relativity and cosmology. In general relativity, gravitational waves consist of only two tensor polarization modes, while some modified theories of gravity propose up to six polarizations. Thus, additional non-tensorial polarizations offer a unique signature of new physics and provide a generic and powerful tool for testing general relativity. In this dissertation, we develop models for the six polarizations possible in modified theories, where these polarizations can propagate at different speeds. These models offer a more straightforward method to obtain the expressions that serve as the foundation for waveform template creation. We apply these models to Einstein-æther theory, a specific theory of modified gravity that allows us to test Lorentz-violation in the gravitational sector -- a feature common to many theories of quantum gravity. For the first time, we construct a waveform template in this theory and test it against gravitational wave data. While we find that current data is insufficient to place more stringent constraints than existent bounds, this work establishes a framework for future tests. Furthermore, to better illustrate the physical phenomenon considered in these works, we also develop novel visualizations of gravitational wave polarizations in virtual reality. These animations allow for a deeper understanding of each polarization individually and their combined effects. Next, we investigate how propagation speeds of different polarizations impact their detectability and examine the implications for current constraints on additional polarizations. We propose a novel search technique for such polarizations, considering how they would correlate with the tensor polarizations that have already been detected. In the event that additional polarizations are not detected, we consider how this non-detection can still inform studies of modified theories by placing limits on the possible values of certain parameters, such as the polarization speeds. Finally, in addition to these tests of modified gravity, we propose a new test of cosmology utilizing the gravitational wave background -- a collection of many faint, unresolvable events. We demonstrate that even in the case of a non-detection, this test can improve our measurement of the expansion rate of the Universe. In combination with spectral siren techniques, this may contribute to the resolution of the current Hubble tension. Overall, this dissertation contributes to the development of new analytical models and data analysis techniques for gravitational waves. Our findings suggest several promising directions for future research, including the development of new waveform templates in modified theories of gravity, searches for time-separated gravitational wave polarizations, and further measurements of the Hubble constant informed by the gravitational wave background.

Graduation Semester

2025-05

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/129467

Copyright and License Information

Copyright 2025 Kristen Schumacher

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