added incomplete introduction

proposal.tex

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-\newcommand{\hmwkDueDate}{{Thesis Proposal}}
+\newcommand{\hmwkDueDate}{Thesis Proposal}
 \newcommand{\hmwkClass}{Probing strong gravity and cosmology using gravitational-wave observations}
 \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}}}
+\newcommand{\hmwkAuthorName}{\textbf{Aditya Vijaykumar}}
+\newcommand{\supervisor}{Supervisor : Prof. Parameswaran Ajith}
+\newcommand{\institute}{
+	\textit{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India}}
 
 
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+\affil{\small{Supervisor: Prof. Parameswaran Ajith \\ \textit{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India}}}
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 \begin{document}
 \begin{document}
 	\maketitle
 	\maketitle
 	
 	
-	\subsection{Introduction}
-	Explain why GWs are great
+	
+	
+	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.\\
+	
+	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 $ \sim 30 M_\odot $ black holes at a distance of xyz Mpc. \textcolor{blue}{Write about GW170817}.
+	\\
+	
+	\textcolor{blue}{Paragraph about Future Dectectors}
+	\\
+	
+	\textcolor{blue}{Segue to description of projects }
 	\subsection{Probing Cosmological Large Scale Structure}
 	\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.
 	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.