Gravitational waves (GWs) are a prediction of Einstein's general theory of relativity \cite{Einstein:1918btx}, and are produced by time varying quadrupole (and higher) moments of a spacetime. When gravitational waves pass through a test mass, they compress it in one direction and stretch it in the orthogonal direction. There are several proposed ways of detecting gravitational waves, but laser interferometers have been the most successful.\\
Gravitational waves (GWs) \cite{Einstein:1918btx} are a prediction of Einstein's general theory of relativity, and are produced by time varying quadrupole (and higher) moments of a spacetime. Gravitational waves interact with test masses by squeezing the test mass in one direction and stretching it in the orthogonal direction. There are several proposed ways of detecting gravitational waves, but laser interferometers (first proposed by Rainer Weiss \cite{weiss1972gravitation}) have arguably been the most successful.\\
When stars run out of their nuclear fuel and are no longer able to support their own gravity, they collapse and form dense, compact objects like black holes and neutron stars. The most promising sources of gravitational waves that can be detected with laser interferometers are the merger of such compact object such as neutron stars and black holes. The mergers produce a signal in the laser interferometers with a characteristic \textit{chirp} morphology \textit{ie}. the amplitude and the freqeuncy of the signal increase with time until the merger is complete. On September 14th, 2015, the Laser Interferometer Gravitational-wave Observatories (LIGO) at Livingston, Lousiana and Hanford, Washington in the United States of America detected gravitational waves from the merger of two $\sim30 M_\odot$ black holes at a distance of xyz Mpc. \textcolor{blue}{Write about GW170817}.
When stars run out of their nuclear fuel and are no longer able to support their own gravity, they collapse and form dense, compact objects like black holes and neutron stars. The most promising sources of gravitational waves that can be detected with laser interferometers are the merger of such compact object such as neutron stars and black holes. The mergers produce a signal in the laser interferometers with a characteristic \textit{chirp} morphology \textit{ie}. the amplitude and the freqeuncy of the signal increase with time until the merger is complete. On September 14th, 2015, the Laser Interferometer Gravitational-wave Observatories (LIGO) at Livingston, Lousiana and Hanford, Washington in the United States of America detected gravitational waves from the merger of two $\sim30 M_\odot$ black holes at a distance of $\sim400$ Mpc \cite{Abbott:2016blz}. This first detection immediately provided constraints on various aspects of physics and astrophysics such as the validity of general relativity \cite{TheLIGOScientific:2016src} and the merger rate of binary black holes (BBHs) \cite{Abbott:2016nhf}. On August 17th, 2017, LIGO along with the Virgo detector in Cascina, Italy also detected a gravitational-wave signal from the merger of two neutron stars at a distance of $\sim40$ Mpc \cite{TheLIGOScientific:2017qsa}. This event was followed up by electromagnetic telescopes all around the world \cite{GBM:2017lvd}, localizing the event inside the galaxy NGC 4993 while also detecting a short gamma-ray burst GRB 170817A and a kilonova powered by the radioactive decay of r-process nuclei synthesized in the merger ejecta. This observation allowed constraints to be placed on the value of the speed of gravitational waves \cite{GBM:2017lvd}, Hubble constant \cite{Abbott:2017xzu}, dark energy and modified gravity \cite{Creminelli:2017sry,Ezquiaga:2017ekz} and the neutron star equation of state \cite{Abbott:2018exr}.
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\textcolor{blue}{Paragraph about Future Dectectors}
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\textcolor{blue}{Segue to description of projects }
\subsection{Probing Cosmological Large Scale Structure}
The next generation of GW detectors will have higher distance reach, and are expected to detect hundreds of thousands of GW events with better localization. If we imagine these detected events to be a ``survey'' akin to a survey of galaxies, we can constrain properties of large-scale structure by measuring the cosmological two-point correlation function. We simulate localization posteriors of future GW events and account for the ``smearing'' of the two-point correlation function due to these localization uncertainties. With this, we show that the bias of the detected BBH population can be measured in a certain redshift range with 3-5 years of observation. These measurements will provide new insights into the type of galaxies that BBHs are hosted in, and could shed light on possible formation channels. Our method does not require the use of galaxy catalogs or electromagnetic counterparts. We are working to extend this to other aspects of large-scale structure.
\subsection{Constraining the time-variation of the gravitational constant}
The next generation of GW detectors will have higher distance reach, and are expected to detect hundreds of thousands of GW events with better localization. If we imagine these detected events to be a ``survey'' akin to a survey of galaxies, we can constrain properties of large-scale structure by measuring the cosmological two-point correlation function. A preliminary analysis has already been done in \cite{Vijaykumar:2020pzn} where we showed that the large-scale bias of the detected BBH population can be measured in a certain redshift range with 3-5 years of observation with third generation detectors. This method does not require the use of galaxy catalogs or electromagnetic counterparts. The measurements hence obtained will serve to provide new insignts into the type of galaxies that BBHs are hosted in. We aim to extend this work by understanding how the measurement of the bias can be used to constrain formation channels of the BBHs. We also aim to make a detection of the Baryon Acoustic Oscillation (BAO) peak from the correlation function of BBHs, and turning this detection into a measurement of cosmological parameters, most notably the Hubble Constant.
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Although the value of $ G $ is constant in the realm of general relativity, a generic class of alternative theories of gravity including scalar-tensor theories like the Brans-Dicke theory permit a time varying $ G $. We place constraints on the time variation of $ G $ using the detected LIGO-Virgo BNS events by noting that the GW signal from BNS observations carry an imprint of $ G=G_{\mathrm{s}}$ at the time of merger, and that the maximum and minimum mass of a neutron star scales as $ m_{\mathrm{min,max}}\sim G_{\mathrm{s}}^{-3/2}$. The constraints thus obtained are fourteen orders of magnitude stronger than the existing constraints from GWs \cite{Yunes:2016jcc} and probe a fundamentally different epoch of cosmic time. These constraints are expected to improve by one or two orders of magnitude with next-generation GW detectors by probing deeper into the cosmos and by stacking constraints at the same cosmological epoch.
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\subsection{Constraining properties of black hole mimickers}
The BBHs detected by LIGO-Virgo are consistent with being BBHs in general relativity; however, there are theoretical proposals of alternatives to black holes, collectively referred to as \textit{black hole mimickers}. These objects can be massive and compact enough so that GWs from their binaries can be confused with those from BBHs; but their GW signal will generically contain an imprint of their tidal deformability $\Lambda$ ($\Lambda=0$ for black holes). In this ongoing work (an extension of \cite{Johnson-McDaniel:2018uvs}), we consider the inspiral regime of the detected BBH events and measure their tidal deformability (or lack thereof). These measurements can be turned into constraints on the equation of state of a given black hole mimicker, thus allowing us to place constraints on the possibility of the detected events being mimickers themselves.
