In this paper we quantify the ability of the Laser Interferometer Space Antenna (LISA) to test the presence of non-tensorial polarizations as well as modifications to the tensor ones in gravitational waves emitted from massive black hole binaries. We employ the Parametrized Post-Einsteinian (PPE) formalism to model deviations from General Relativity (GR) for tensor, vector, and scalar polarizations. Our PPE parametrization is inspired by post-Newtonian waveforms from four modified gravity theories: Horndeski, Einstein-aether, Rosen’s bimetric, and Lightman-Lee. We consistently implement these modifications across the inspiral, merger, and ringdown phases, ensuring proper waveform alignment and tapering. Subsequently, we perform Fisher forecasts to derive expected constraints on deviations from General Relativity and map these constraints to the parameter spaces of the four gravity theories. For tensor polarizations, LISA achieves constraints on amplitude modifications ranging between ∼10⁻⁴–10⁻² precision level, depending on the frequency evolution of the modifications, for systems with 10⁵–10⁷ M_⊙ at z = 1. We find that LISA can distinguish breathing and longitudinal scalar polarizations only for relatively light binaries with M ≲ 10⁴ M_⊙, beyond which these modes become degenerate in the detector response. Importantly, constraints on vector polarizations are approximately 2-3 times more precise than for scalar polarizations. For both vector and scalar modes, amplitude measurements reach precisions ranging between ∼10⁻⁸–10⁻², depending on the frequency evolution of the modifications, for systems with 10⁵–10⁷ M_⊙ at z = 1. These results demonstrate LISA’s potential to probe gravity in the strong-field regime via gravitational wave polarizations.

Gravitational waves from individually resolved compact object mergers can be used as standard sirens, offering a novel self-calibrating precision probe of cosmology. While the standard siren method has been well-explored, the gravitational-wave background arising from unresolved mergers offers a novel alternative to probing cosmology. We demonstrate that the combination of resolved binary black hole mergers with the unresolved signals composing the stochastic gravitational-wave background can be used to measure cosmological parameters, including the Hubble constant, H₀. We apply this “stochastic siren” method to existing gravitational-wave data and find that including the current non-detection of the background increases the accuracy at which H₀ can be measured, relative to using resolved mergers alone. We also provide projections for upcoming detectors to highlight their ability to probe cosmology with the background. With the anticipated detection of the astrophysical gravitational-wave background, the stochastic siren approach can be expected to improve future standard siren cosmological measurements.

In some beyond-Einstein theories of gravity, gravitational waves can contain up to six polarizations, which are allowed to propagate at different speeds faster than light. These different propagation speeds imply that polarizations generated by the same source will not arrive simultaneously at the detector. Current constraints on the speed of propagation of transverse-traceless polarizations, however, indicate that any additional polarizations must arrive with or before the transverse-traceless ones. We propose a new technique to test for the existence of superluminal, non-transverse-traceless polarizations that arrive in the data before a gravitational-wave observation of transverse-traceless modes. We discuss the circumstances in which these non-transverse-traceless polarizations would be detectable and what constraints could be placed if they are not detected. To determine whether this new test of general relativity with gravitational wave observations is practical, we outline and address many of the challenges it might face. Our arguments lead us to conclude that this new test is not only physically well-motivated but also feasible with current detectors.

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.

In some modified theories of gravity, gravitational waves may contain up to six polarizations. These different polarizations determine the pattern with which the gravitational waves stretch and squeeze spacetime, both perpendicular to and along the direction of propagation. Given the multi-dimensional nature of these distortions and the fact that they are not visible to the naked eye, immersive virtual reality is a useful tool for visualizing them. In this work, we introduce what we believe is the first visualization tool allowing users to explore all six gravitational wave polarizations. This interactive and immersive virtual reality experience features three different visualization modes intended to illustrate the different patterns of distortion for each polarization, for arbitrary combinations of the polarizations, and for combinations of polarizations that correspond to specific theories of gravity.

Lorentz symmetry is a fundamental property of Einstein’s theory of general relativity that one may wish to test with gravitational wave observations. Einstein-æther theory is a model that introduces Lorentz-symmetry breaking in the gravitational sector through an æther vector field, while still leading to second-order field equations. This well-posed theory passes particle physics constraints because it modifies directly only the gravitational sector, yet it predicts deviations in the inspiral and coalescence of compact objects. We here, for the first time, put this theory to the test by comparing its gravitational wave predictions directly against LIGO/Virgo gravitational wave data. We first construct a waveform model for Einstein-æther theory, EA_IMRPhenomD_NRT, through modifications of the general relativity IMRPhenomD_NRTidalv2 model (used by the LIGO/VIRGO collaboration). This model constructs a response function that not only contains the transverse-traceless polarization but also additional Einstein-æther (scalar and vectorial) polarizations simultaneously. We then use the many current constraints on the theory to construct nontrivial priors for the Einstein-æther coupling constants. After testing the waveform model, we conduct parameter estimation studies on two gravitational wave events: GW170817 and GW190425. We find that these data are not sufficiently informative to place constraints on the theory that are stronger than current bounds from binary pulsar, Solar System, and cosmological observations. This is because, although Einstein-æther modifications include additional polarizations and have been computed beyond leading post-Newtonian order, these modifications are dominated by (already-constrained) dipole effects. These difficulties make it unclear whether future gravitational wave observations will be able to improve on current constraints on Einstein-æther theory.

In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are important because any detection would be clear evidence of new physics, while clear nondetections could constrain some modified theories. The first step toward searching the data for such gravitational wave content is the calculation of the amplitudes of these different polarizations. Here we present a model-independent method to obtain the different polarizations of gravitational waves directly from the metric perturbation in theories where these polarizations are allowed to travel at different speeds. We develop our calculations so that the same procedure works with either the metric perturbation itself or its trace-reversed form. Our results are in agreement with previous work in the limit that all polarization speeds are the speed of light. We demonstrate how our model-independent method can be used with two specific modified theories of gravity, suggesting its wide applicability to other theories that allow for different gravitational wave propagation speeds. We further extend the parametrized post-Einsteinian formalism to apply to such theories that travel with different speeds. Finally, we discuss how the different speeds of different polarizations may affect null stream tests of general relativity with gravitational wave observations by multiple interferometers. Differences in propagation speeds may make null streams ineffective or lead to the detection of what seem to be isolated scalar or vector modes.

According to general relativity, gravity can be understood as a curvature of spacetime in response to the presence of matter and energy. Students often struggle to visualize the geometry of curved spacetime. The standard demonstration used to aid in visualization, that of a ball on an elastic sheet, is fundamentally flawed and may lead to misconceptions. Recent research suggests that virtual reality can improve understanding of spatially complex or abstract concepts. We hypothesize that an interactive virtual reality demonstration involving masses in a curved 3D spatial grid, with clocks representing the relative passage of time, would support improved conceptual understanding and impact attitude among students learning general relativity compared to traditional methods. To test this hypothesis, undergraduate students who have no formal experience with general relativity are recruited to evaluate the virtual reality simulation. The students first take a questionnaire to determine a baseline for their conceptual understanding of general relativity, with confidence-scaled multiple choice and written response questions. The experimental group experiences an interactive virtual reality demonstration in which the subjects can move objects through space and time to visualize how mass curves spacetime. An instructor leads the control group through the standard ball on a sheet demo while delivering content orally. Students in both groups are prompted by an instructor to explore the relationship between mass, gravity, and time, guided by a set of conceptual questions. Immediately after the demonstrations, students complete the same questionnaire and a survey about learner attitude and simulation usability. Few previous studies focus on the conceptual understanding of general relativity and even fewer examine the possibility of immersive learning as a tool for teaching this topic. Our work addresses this gap by designing a novel immersive technique for visualizing relativistic effects and comparing this technique to existing non-immersive methods of instruction.

The Mu2e experiment at Fermilab will search for the neutrinoless μ⁻ → e⁻ conversion in the field of an aluminum nucleus. The Mu2e data-taking plan assumes two running periods, Run I and Run II, separated by an approximately two-year-long shutdown. This paper presents an estimate of the expected Mu2e Run I search sensitivity and includes a detailed discussion of the background sources, uncertainties of their prediction, analysis procedures, and the optimization of the experimental sensitivity. The expected Run I 5σ discovery sensitivity is R_μe = 1.2 × 10⁻¹⁵, with a total expected background of 0.11 ± 0.03 events. In the absence of a signal, the expected upper limit is R_μe < 6.2 × 10⁻¹⁶ at 90% CL. This represents a three order of magnitude improvement over the current experimental limit.

The NICER Collaboration recently reported the measurement of the mass and radius of a pulsar PSR J0030+0451. We here use this new measurement to constrain one of the higher-order nuclear matter parameters K_sym,0. We further combine the tidal measurement of the binary neutron star merger GW170817 by LIGO/Virgo to derive a joint 1-σ constraint as K_sym,0 = −102⁺⁷¹₋₇₂ MeV. We believe this is the most reliable bound on the parameter to date under the assumption that there is no new physics above the saturation density which impacts neutron star observations.