Hi,

I am international applicant for PhD in astronomy. Below is a draft of my SOP, which I feel is too long and am concerned about the flow.Kindly review it.

---

After four years of undergraduate education, during which I spent time trying my hands at various academic and non academic endeavours, I wish to pursue graduate studies in Astronomy at XXXX , in order to streamline my interests and build expertise in Astrophysics and Cosmology.

Being an Engineering Physics undergraduate gave me the opportunity to study both science and engineering. While my electrical engineering peers only knew how a MOSFET or BJT can be used, we, as physics students could comprehend how quantum mechanics and statistical physics are elementary to the functioning of these devices. This made me love science more than technology. The Department of Physics here at XXX has deepened this interest by exposing me to various research activities through weekly science colloquia and this was how I was introduced to some of the open questions of modern day Physics. Driven by a problem solving attitude, I started exploring those questions and due to my added interest in history, I was attracted to learning about the past of our Universe. I spoke to one of my course instructors, Prof.ABC, about my interests and he referred me to a few books, Prof. Steven Weinberg’s “The First Three Minutes” being one of them, through which I understood the build-up to the present Lambda CDM model, beginning with the static model, to the discovery of Cosmic Microwave Background ,the Big Bang theory and introduction of dark matter and dark energy to explain CMB anisotropies and large scale structure . This helped me in understanding the nature of scientific research and made me realize how it takes a number of theories, number of people and years of efforts, to establish a firm theory which could not only justify observations but also makes predictions that can be tested. Research requires perseverance, which I believe I had in solving Math and Physics problems since high school, which made me not only top my school but also stand among the top 1 % in every reputed national and state wide engineering entrance test I took in my country.

Further, I taught myself basics of General Relativity in order to lay the framework to understand Cosmology. As a part of short course taught by Prof. XXXX, I’ve attended lectures on background cosmology where the Standard Model was discussed. To experience research in Cosmology, I applied to the Visiting Student program at XXXXXX and got selected to work under Professor YYYY, who does Cosmology with Large Scale Structure of the Universe. The fact that the matter we know of contributes to only 5% of the total is something which has always intrigued me and so I expressed this fascination towards dark matter to him, and was assigned to work on a project that was related to understanding an important stage in the bottom-up hierarchy of structure formation: the non-linear evolution of dark matter density perturbations. I studied the Spherical Collapse model, the results of which are useful in computing the number density of dark matter halos as a function of their mass and redshift(Press Schechter formalism). The Spherical Collapse model gives an easier way to study gravitational collapse, without actually having to solve the Euler's equation, a nonlinear equation which can't yet be solved analytically without approximating. Using the Spherical Collapse model, I have analytically solved for the density contrast at which gravitational collapse occurs, resulting in the formation of dark matter halos. I have also derived the density contrast at which shell crossing occurs in Voids, the under dense counterparts of halos. As a part of the visiting student program, I have also attended the refresher course in Astrophysics, which introduced me to various topics in the forefront of present day Astronomy and Astrophysics through lectures and demonstrations.

Currently, I am working on my Bachelor thesis titled”----”. Until now, I have learnt about the relativistic cosmological perturbation theory to arrive at the perturbed Einstein’s equations and reduced them to get a single equation for the Bardeen potential .Using conservation of perturbed stress energy tensor, I derived the relativistic fluid equations. To understand the evolution of matter and radiation density perturbations during radiation and matter dominated epochs, before and after they enter the horizon, I solved the above equations. These solutions have been used to arrive at the transfer function and the dark matter power spectrum. I’ll be looking for a good fit to the observed dark matter power spectrum deduced from CMB using CAMB python and compare it to the above derived power spectrum. In the coming December, I’ll be attending a week-long course& workshop on “Darkmatter-the astroparticle perspective” taught by Prof. XXX, through which I hope to learn more about the astrophysical and cosmological background to the dark matter problem and candidate particles arising in models of new physics, as well as about attempts to detect them by both direct and indirect means. Next semester, I’ll be taking courses on General Relativity and Particle Physics. With that, I’ll also be on track to get an Honors degree.

In summary, I feel that I’ve developed a strong foundation in theoretical Cosmology over the last two years and would like to employ my skills in tackling unresolved issues related to the identity of dark matter, from an astrophysical perspective. The Astronomy department at XXX has an active theory/observational group working towards testing theories of cold dark matter on small scales etc..(to be modified depending on grad school)