We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this ...method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, \(H_0\), when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.
We analyze the confident binary black hole (BBH) detections from the third
Gravitational-Wave Transient Catalog (GWTC-3) with an alternative mass
population model in order to capture features in the ...mass distribution beyond
the Powerlaw + Peak model. We find that the peak of a second power law
characterizes the $\sim 30-35~ M_\odot$ bump, such that the data marginally
prefers a mixture of two power laws for the mass distribution of binary
components over a Powerlaw + Peak model with a Bayes Factor
$\log_{10}\mathcal{B}$ of 0.1. This result may imply that the $\sim 30-35~
M_\odot$ feature represents the onset of a second population of BBH mergers
(e.g. from a dynamical formation channel) rather than a specific mass feature
over a broader distribution. When an additional Gaussian bump is allowed within
our power law mixture model, we find a new feature in the BH mass spectrum at
$\sim65-70~M_\odot$. This new feature may be consistent with hierarchical
mergers, and constitute $\sim2\%$ of the BBH population. This model also
recovers a maximum mass of $58^{+30}_{-14}~M_\odot$ for the second power law,
consistent with the onset of a pair-instability supernova mass gap.
Since the first detection of gravitational waves (GWs) from the merger of two stellar-mass black holes in 2015, the LIGO-Virgo-KAGRA (LVK) Collaboration has accumulated over 90 observations of ...mergers involving neutron stars and black holes. With the upcoming observing runs for the LVK network of GW detectors, many more binary mergers are expected to be detected. The increasing size of gravitational wave catalogs has enabled the study of their population, its cosmic expansion history, signatures of gravitational wave lensing, and how well these observations agree with general relativity. In this dissertation, I will discuss my contributions to gravitational wave cosmology. I will focus on the development of the dark siren methodology and how it was used with the GWTC-1 catalog to provide a first joint measurement of the Hubble constant from GW standard sirens. I will also discuss a joint parameter estimation framework developed to identify and characterize pairs of strongly lensed GWs from binary black hole mergers and how it was was applied to GWTC-1 observations. Finally, I will explore two topics related to testing modifications to general relativity. First, I will describe how we used the strong lensing joint parameter estimation framework to measure the presence of alternative polarization modes in GW signals from BBH mergers, including a fully mixed tensor, vector, and scalar mode model. Second, I will discuss my work on modified GW propagation in the context of gravitational leakage models, which predict the existence of large extra spacetime dimensions. Using the latest GWTC-3 catalog, we provided the first constraints on such extra-dimension models using BBH mergers.
In modified gravity models that allow for additional non-compact spacetime dimensions, energy from gravitational waves can leak into these extra spacetime dimensions, leading to a reduction in the ...amplitude of the observed gravitational waves, and thus a source of potential systematics in the inferred luminosity distances to gravitational wave sources. Since binary black hole (BBH) mergers are standard sirens, we use the pair-instability supernova (PISNe) mass gap and its predicted features to determine a mass scale and thus be able to break the mass-redshift degeneracy. We simultaneously fit for the BBH population and the extra spacetime dimensions parameters from gravitational leakage models using BBH observations from the recently released GWTC-3 catalog. We set constraints on the number of spacetime dimensions and find that \(D= 3.95^{+0.09}_{-0.07}\) at \(68\%\) C.L. for models that are independent of a screening scale, finding that the GWTC-3 constraint is as competitive as that set from GW170817 and its electromagnetic counterpart. For models where gravity leaks below a certain screening scale \(R_c\), we find \(D=4.23^{+1.50}_{-0.57}\) and \(\log_{10} R_c/{\rm Mpc}= 4.14^{+0.55}_{-0.86}\) with a transition steepness \(\log_{10} n = 0.86^{+0.73}_{-0.84}\) for the leakage, which for the first are constrained jointly with the BBH population at cosmological distances. These constraints are consistent with General Relativity (GR) where gravitational waves propagate in \(D=3+1\) spacetime dimensions. Using the BBH population to probe modifications to standard cosmological models provides an independent test of GR that does not rely on any electromagnetic information but purely on gravitational wave observations.
The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant \(H_0\) using gravitational wave standard sirens. When ...no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate \(H_0\) using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of \(H_0\). Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of \(H_0\), as well as the effect of weighting each galaxy's likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4\% measurement precision can be reached using galaxy catalogs with 50\% completeness and \(\sim 250\) binary neutron star detections with sensitivity similar to that of Advanced LIGO's second observing run.
We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this ...method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, $H_0$, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.
It is expected that gravitational waves, similar to electromagnetic waves, can be gravitationally lensed by intervening matters, producing multiple instances of the same signal arriving at different ...times from different apparent luminosity distances with different phase shifts compared to the un-lensed signal due to lensing. If unaccounted for, these lensed signals will masquerade as separate systems with higher mass and lower redshift. Here we present a Bayesian statistical framework for identifying strongly-lensed gravitational-wave signals that incorporates astrophysical information and accounts for selection effects. We also propose a two-step hierarchical analysis for more efficient computations of the probabilities and inferences of source parameters free from bias introduced by lensing. We show with examples on how changing the astrophysical models could shift one's interpretation on the origin of the observed gravitational waves, and possibly lead to indisputable evidence of strong lensing of the observed waves. In addition, we demonstrate the improvement in the sky localization of the source of the lensed signals, and in some cases the identification of the Morse indices of the lensed signals. If confirmed, lensed gravitational waves will allow us to probe the Universe at higher redshift, and to constrain the polarization contents of the waves with fewer detectors.
We analyze the confident binary black hole (BBH) detections from the third Gravitational-Wave Transient Catalog (GWTC-3) with an alternative mass population model in order to capture features in the ...mass distribution beyond the Powerlaw + Peak model. We find that the peak of a second power law characterizes the \(\sim 30-35~ M_\odot\) bump, such that the data marginally prefers a mixture of two power laws for the mass distribution of binary components over a Powerlaw + Peak model with a Bayes Factor \(\log_{10}\mathcal{B}\) of 0.1. This result may imply that the \(\sim 30-35~ M_\odot\) feature represents the onset of a second population of BBH mergers (e.g. from a dynamical formation channel) rather than a specific mass feature over a broader distribution. When an additional Gaussian bump is allowed within our power law mixture model, we find a new feature in the BH mass spectrum at \(\sim65-70~M_\odot\). This new feature may be consistent with hierarchical mergers, and constitute \(\sim2\%\) of the BBH population. This model also recovers a maximum mass of \(58^{+30}_{-14}~M_\odot\) for the second power law, consistent with the onset of a pair-instability supernova mass gap.
We perform Bayesian model selection with parameter estimation to identify potentially lensed gravitational-wave images from the second observing run (O2) of Advanced LIGO and Advanced Virgo. ...Specifically, we compute the Bayesian evidence for a pair of events being lensed or not lensed (unlensed) using nested sampling. We consider the discrete coalescence phase shifts that can be induced if the gravitational-wave signal interacts with the lens caustics in the model selection. We find that the pair of events, GW170104 and GW170814 with a \(\pi/2\) coalescence phase shift, has a significant Bayes factor (\(B^L_{U}\) \(\sim 1.98 \times 10^4\)) favoring the lensing hypothesis. However, after taking into account the long time delay of approximately 7 months between events, the timing Bayes factor is significantly small (\(B_t \sim 8.7\times10^{-2}\)). The prior probability for detecting strongly lensed pairs at O2 sensitivity are exceedingly small for both galaxy and galaxy cluster lensing. Combining the lensing and timing Bayes factors with the prior odds on lensing gives an odds ratio of \(O^L_{U} \sim 20\). However, the model dependence of the timing and prior odds factors does not provide strong evidence to demonstrate that the pair is strongly lensed.
The discovery of the coalescence of binary neutron star GW170817 was a watershed moment in the field of gravitational wave astronomy. Among the rich variety of information that we were able to ...uncover from this discovery was the first non-electromagnetic measurement of the neutron star radius, and the cold nuclear equation of state. It also led to a large equation of state model-selection study from gravitational-wave data. In those studies Bayesian nested sampling runs were conducted for each candidate equation of state model to compute their evidence in the gravitational-wave data. Such studies, though invaluable, are computationally expensive and require repeated, redundant, computation for any new models. We present a novel technique to conduct model-selection of equation of state in an extremely rapid fashion (~minutes) on any arbitrary model. We test this technique against the results of a nested-sampling model-selection technique published earlier by the LIGO/Virgo collaboration, and show that the results are in good agreement with a median fractional error in Bayes factor of about 10%, where we assume that the true Bayes factor is calculated in the aforementioned nested sampling runs. We found that the highest fractional error occurs for equation of state models that have very little support in the posterior distribution, thus resulting in large statistical uncertainty. We then used this method to combine multiple binary neutron star mergers to compute a joint-Bayes factor between equation of state models. This is achieved by stacking the evidence of the individual events and computing the Bayes factor from these stacked evidences for each pairs of equation of state.
