added first set of files; copied text from flatiron research summary

proposal.tex

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+
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+\newcommand{\hmwkTitle}{}
+\newcommand{\hmwkDueDate}{{Thesis Proposal}}
+\newcommand{\hmwkClass}{Probing strong gravity and cosmology using gravitational-wave observations}
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+\newcommand{\hmwkAuthorName}{\textbf{Aditya Vijaykumar, \textit{International Centre for Theoretical Sciences}}}
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+% Alias for the Solution section header
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+
+\begin{document}
+	\maketitle
+	
+	\subsection{Introduction}
+	Explain why GWs are great
+	\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}
+	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.
+	
+	\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.
+
+\bibliography{references}
+\bibliographystyle{jhep}
+\end{document}
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