Here is a rough draft of my SOP, which I wrote today. I am aware that the ending (the goals part) isn't very well-formed right now. I would be glad if someone could review / critique this for me:
The way math described the physical world in a predictive and self-consistent way had appealed to me since a class project on gravity in grade 11. I enjoyed learning high school physics, and I aced the physics section on the highly competitive Joint Entrance Examination for the Indian Institutes of Technology. I was still unsure about physics as a career, and thus chose the “conventional” engineering major at the Birla Institute of Technology and Science, Pilani.
At BITS, I realized the full extent of my affinity towards physics, and the university offered me the freedom to take reading courses as electives. I started with relativity, about which I had always been curious, learning it from a combination of books and online lectures. Fired by the revelation of the significance of Einstein’s equations, I then self-studied basic cosmology, a branch of physics I thought asked the biggest questions, and started a project on plotting the Hu-Eisenstein power spectrum under Dr. Tapomoy Guha Sarkar.
In my junior year, I attended a school on advanced cosmology, with lectures on structure formation, inflation and dark energy. How a field of random fluctuations gave rise to the structures we see today was a moment of revelation for me, and inflation struck me as an elegant solution to a host of issues with the big bang model, which still lacked many answers. Driven by this, I started my bachelor’s thesis at the National Centre for Radio Astrophysics under Dr. Tirthankar Roy Choudhury. I studied the halo model, and then learned N-body simulations with GADGET-2. I then modified an initial conditions generation code to include massive neutrinos, and ran simulations to assess the impact of the same on the power spectrum at small scales.
I had composed an international trivia quiz, organized a national cultural festival, published regularly in the college magazine, written papers on Kashmiri literature, and lectured on control systems and signals and systems apart from my physics projects, but I felt I was not ready for graduate school. I decided to take a year off, during which I studied the HI power spectrum, wrote code for the halo model power spectrum, and an integrated suite for power spectrum and halo mass function calculations. I also started reading more about dark energy, and then modified the GADGET-2 code to include some simple quintessence cosmologies. I also built my own cricket statistics database, and formulated new statistics, Moneyball style, to gauge performances, including using survival analysis to extend censored “not-out” innings.
I decided that I needed a firm base and well-rounded view, through a formal education in physics, and joined the master’s program at Jawaharlal Nehru University. Where I had been disillusioned with courses in my undergrad, I started enjoying learning physics properly, topping classical mechanics, both my mathematical physics courses, relativity and statistical physics. I did an optional term paper and presentation for Dr. Ram Ramaswamy on classical fields to start with quantum field theory, and continued studying the same under Dr. Debashish Ghoshal as I wanted to explore theoretical cosmology, through studying inflation. I am now starting my master’s project on effective field theory techniques in inflation and dark energy.
My progress gave me confidence, which was bolstered further when I was awarded the prestigious Summer Research Fellowship by the Indian Academy of Sciences. I spent the summer of 2017 working under Dr. Jasjeet Singh Bagla at the Indian Institute of Science Education and Research, Mohali. I generated initial conditions using a scale-invariant power spectrum, and ran a suite of simulations in an Einstein-deSitter cosmology using GADGET-2, to investigate the dependence of the Sheth-Tormen mass function parameters on the tilt of the power spectrum. In the most productive two months of my life, I felt at home in research, modeling it as a cascade of problems I enjoyed solving. This was also the first time I used statistics for actual inference and fitting. On the side, I adapted codes for the power spectrum and correlation function, and also started a project with a student of Dr. Bagla’s, where I am using my modified GADGET-2 code to plot the halo mass – angular momentum relation in some quintessence cosmologies.
My stints at NCRA and IISER, along with my independent projects in physics and otherwise, have convinced me that I am best suited for research: I enjoy and work best with formulating and attacking problems. I believe that simulations are going to be the single most powerful tool in the future, since the universe is the only instance, and experiments are limited. The questions of dark energy and inflation are still unsolved in cosmology, as it enters an exciting era with abundant data and computational power. I want to use my graduate education to further pursue these questions as a career, and also teach, which I believe is important to learn, as well as continue encouraging people to take up such questions in the future.
I have explored a wide variety of fields within cosmology, and mainly want to use simulations to confirm new models, of dark energy, inflation and structure formation. I believe I am suited to graduate work in cosmology, with my experience in theory and simulations, my work in statistics, and my previous background in electrical engineering, which is a suitable combination for a field that now involves working in everything. Moreover, I believe I have the tenacity and self-learning ability to succeed in graduate school and research, as evidenced by my journey from an engineering major to physics.
<Insert department-specific portion here: will contain more specific work goals / might have to condense with the above paragraph.>