My Statement of purpose has some grammar mistakes in it I know that. However I have access to a writing center for free so as now I'm not interested in critiques of the grammar. Ideally I would like critiques on the content, specifically whether I show that my undergraduate experience has prepared me for the type of research I lay out I want to do in graduate school.

My goal is to research whether or not the accelerated expansion of space can be accounted for by quantum fluctuations predicted by Quantum Field Theory. Recent work in modified gravity, such as the DGP model has spurred my interest in this problem because it can explain the observed acceleration of space without postulating dark energy. I would like to conduct theoretical research in these models to determine if they can explain the value of the cosmological constant

In college, my drive to become a professor, and hence teach began when I became a physics tutor. As a tutor, I would show my students the derivation of equations, as opposed to just applying them. What I enjoyed most from tutoring is seeing students' faces light up when they understood something in more detail than they thought possible. Eventually I became the physics tutors’ Team Leader, thus assuming the responsibility of making and grading mock exams. This meant I had to understand what students that were taking the introductory physics sequence were struggling with so I can make more appropriate exams. While I was Team Leader, I assumed many of the functions of a lecturer and enjoyed the experience. In light of everything I want to become a professor and conduct research in theoretical physics.

My research experience consists of working with Professor David Mugglin at the New York University Polytechnic School of Engineering for three semesters on the dynamics of a physical double pendulum. (PDP). While doing research I learned invaluable lessons. For example the equations of motion I solved and animated are not equivalent to what I built in the lab. From considering this, I learned how to manipulate theoretical models so they can more accurately represent what is being studied. Also, I learned many advanced mathematical and programming techniques, which will be useful in research I do in the future. Applying these techniques taught me how to extract as much information as I can from a mathematical model.

While conducting research, I completed a graduate physics class at the Graduate School of Arts and Science (GSAS). I further incorporated the theories and programming techniques I learned in that class in my research. During my last semester of research in order to graduate on time I had to complete 29 credits of course material while working two jobs. That experience taught me how to further manage time as efficiently as possible and distinguish important results or observations from trivial ones during research.

Professor Mugglin gave me freedom to analyze the dynamics of a PDP. As a result, I decided to study the topological aspects of its phase space in terms of the KAM theorem. In particular, I made a Poincare section simulation that demonstrated how invariant tori disintegrated as I varied a parameter. While doing so, I learned the importance of using computational methods to witness the consequences of a theory. Prior to my research, I downplayed the importance of numerical methods in theory. But after conducting my research I now strive to use computational methods to bring the theory I’m studying to life.

The GSAS of New York University is a good fit for me because it hosts the Center For Cosmology and Particle Physics (CCPP.) The CCPP has pioneered models, which explain cosmic acceleration without dark energy such as the DGP. As a result, it is the ideal place for me to conduct research in determining if dark energy is needed to explain cosmic expansion.

Currently, I’m interested in working with either professor Mathew Kleban or Roman Scoccimarro. Mathew Kleban’s research in quantum gravity interests me because it can shed light on why QFT does not give the correct prediction for the energy density in the vacuum. Professor Scoccimarro’s research on modifying General Relativity (GR) to account for the cosmological constant is of great interest because it can determine whether or not modified gravity can explain the value of the cosmological constant without dark energy.