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.\\
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 mass-energy distributions. Gravitational waves interact with test masses by squeezing the spacetime 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 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, Louisiana 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 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}.
When massive 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 objects. These 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, Louisiana 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 speed of gravitational waves \cite{GBM:2017lvd}, Hubble constant \cite{Abbott:2017xzu}, cosmological models of dark energy and modified gravity \cite{Creminelli:2017sry,Ezquiaga:2017ekz} and the neutron star equation of state \cite{Abbott:2018exr}.
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The LIGO and Virgo detectors are expected to be upgraded to their design sensitivities in the next few years \cite{TheLIGOScientific:2014jea,TheVirgo:2014hva}. The KAGRA detector in Japan \cite{Aso:2013eba,Akutsu:2020his} and LIGO-India \cite{Iyer:LIGOIndia} are also expected to come online in the current decade. Moreover, the next generation of ground-based detectors including Einstein Telescope \cite{Punturo:2010zza,Hild:2010id} and Cosmic Explorer \cite{Evans:2016mbw, Reitze:2019iox} is expected to go online in the next decade. All these improvements would enable the detection of hundreds of thousands of compact binary detections with much better localization \cite{Vitale:2016icu,Mills:2017urp}, thus opening up immense possibilities for doing precision astrophysics\cite{}.
The LIGO and Virgo detectors are expected to be upgraded to their design sensitivities in the next few years \cite{TheLIGOScientific:2014jea,TheVirgo:2014hva}. The KAGRA detector in Japan \cite{Aso:2013eba,Akutsu:2020his} and LIGO-India \cite{Iyer:LIGOIndia} are also expected to come online in the current decade. Moreover, the next generation of ground-based detectors including Einstein Telescope \cite{Punturo:2010zza,Hild:2010id} and Cosmic Explorer \cite{Evans:2016mbw, Reitze:2019iox} is expected to go online in the next decade. All these improvements would enable the detection of hundreds of thousands of compact binary detections with much better localization \cite{Vitale:2016icu,Mills:2017urp}, thus opening up immense possibilities for doing precision astrophysics.
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In this thesis, we shall attempt to explore a few possibilities of probing strong gravity and cosmology using observations of gravitational waves from future detectors. 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 at $ z \lesssim0.7$ using 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.
In this thesis, we shall attempt to explore a few possibilities of probing strong gravity and cosmology using observations of gravitational waves from current and future detectors. If we imagine these detected events to be a ``survey'' akin to the electromagnetic 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 at $ z \lesssim0.7$ using 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 compact binary mergers, and turning this detection into a measurement of cosmological parameters, most notably the Hubble Constant.
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The BBHs detected by LIGO-Virgo are consistent with being BBHs in general relativity \cite{LIGOScientific:2019fpa}; however, there are theoretical proposals of alternatives to black holes, collectively referred to as \textit{black hole mimickers}\cite{Cardoso:2019rvt}. 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). Following the prescription in \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.
Gravitational wave observations also enable unique probes of the nature of gravity and might enable us to detect new types of compact objects, if they exist. The BBHs detected by LIGO-Virgo are consistent with being BBHs in general relativity \cite{LIGOScientific:2019fpa}; however, there are theoretical proposals of alternatives to black holes, collectively referred to as \textit{black hole mimickers}\cite{Cardoso:2019rvt}. 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). Following the prescription in \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.
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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 \cite{BSTheory} 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}$\cite{Vijaykumar:2020nzc}. 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.
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 \cite{BSTheory} permit a time varying $ G $. We can 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}$\cite{Vijaykumar:2020nzc}. 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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This thesis will include a collection of different probes of strong gravity and cosmology using current and upcoming observations mentioned above. We will formulate these problems, develop GW data analysis methods for addressing them, and derive results using appropriate GW data whenever they become available. Some of the probes will require data from the proposed third-generation GW detectors, and these studies will contribute to the science case of these proposed detectors.
