Although it’s a little bit embarrassing, after some consideration, I decide to share my Statement of Purpose (SOP) for PhD application with you. If you find it is useful or you have some comments about it, you are welcome to leave your comments on this article.
During my undergraduate study, I was deeply moved by two plots. The first one is the specific heat in a solid with Einstein’s and Debye’s prediction on it. The second is the CMB power spectrum. I am impressed at how the theoretical predictions can explain the experimental results so precisely when the model captures the important feature of the system. They realize the famous quote “The most incomprehensible fact about the Universe is that it is comprehensible” in a compelling way that makes me want to be a theoretical physicist.
Nowadays, we already have the Lambda-CDM model that explains the evolution of our Universe. However, to explain the observed data, it requires the existence of 95% unknown stuff in our Universe, including 27% dark matter and 68% dark energy. To understand how physicists treat these unknown components, I got involved in a theoretical work about dark matter direct detection as my undergraduate research project. Supervised by Prof. Chuan-Ren Chen, who is a high energy physics phenomenologist, I learned how to calculate the scattering amplitude between ordinary matters in a detector and the dark matter candidates with Feynman diagrams. It was the first time I felt that the calculation I did could be useful to reveal the mystery of the Universe. More importantly, I learned the way how particle physicists treat the dark matter problem.
After graduation, during my compulsory military service, LIGO announced the astonishing detection of GW150914. Again, the theoretical waveform on the plot matched the observed signals so nicely that it is just too good to be true. It provides a brand new way, alongside the neutrino and electromagnetic waves, to observe the history of our universe and I should participate in it. So, I started my master’s degree study. Joining a study group in Taipei Gravitational Wave Group (TGWG), I learned numerical relativity and how to analyze gravitational-wave data of compact binary coalescence events. At that time, I noticed the communication between experimentalists and theorists is not as deep as it should be. Without having real experiences on an experimental project, it is practically hard to fully understand why the experiment was conducted in a particular way, how we should interpret the data, and how theorists can provide their ideas in a way that can be realized in the future experiments. Therefore I decided to join the experiment in Kamioka Gravitational Wave Detector (KAGRA) in Japan.
The main topic of my dissertation is designing and fabricating a frequency-dependent signal attenuator in the KAGRA Photon Calibrator (PCal) system so that we can inject stronger calibration lines into the interferometer without contaminating the sensitivity curve of KAGRA. With the stronger PCal lines, it is possible to reduce the uncertainty of the reconstructed h(t), which may be directly translated into the estimated parameters of GW events. By working in the KAGRA calibration group, I learned not only some practical skills (e.g. Printed Circuit Board Layout), but also how gravitational waves strain data could be reconstructed from the feedback control loop through the real-time digital control system.
After finishing my master’s degree, I started to work at the Academia Sinica in Taiwan as a research assistant. In addition to helping the maintenance of KAGRA data mirroring to the Academia Sinica Grid-computing Centre (ASGC), a Tier-1 of KAGRA, I began to work with Prof. Kin-Wang Ng and Prof. Guo-Chin Liu, who is the chair of the Stochastic Background Working Group in KAGRA, on a topic about stochastic gravitational waves background (SGWB). We studied how to analyze the anisotropic and polarized SGWB by investigating the correlation between GW strain data from different detectors in the spherical harmonic basis. It turns out that my experiences in KAGRA substantially helped me to understand the structure of correlated data. While the work is still ongoing, I believe I am ready for pursuing my PhD degree in theoretical physics. Especially, I am interested in what happened in the early Universe.
Although the possibly existed inflation can answer several observed facts that cannot be solely explained by the Hot Big Bang, for example, the tiny but non-zero CMB anisotropy, the underlying reality of the inflaton field is not clear at the moment, which is similar to the case of dark energy and dark matter. If we do not see the B-mode polarization in the upcoming experiments such as LiteBIRD, will the inflation still be the most viable solution to the horizon and flatness problem? Or can the way of how we estimate the primordial quantum fluctuation have some flaws? Also, regarding the black hole mergers that we are going to detect, could they be primordial black holes? Can black holes serve a significant amount of cold dark matter? What can be the hidden nature of dark energy? All of these are fascinating questions.
On the other hand, concepts developed in the condensed matter physics field might be helpful to understand the early Universe. It is well-known that spontaneous symmetry breaking plays an important role in both high energy physics (Higgs mechanism), and condensed matter physics (BCS theory). I believe that some success in the condensed matter field theory might be useful to solve the problem in cosmology.
In the stage of my PhD study, I would like to work on topics related to quantum effects in the early Universe. At the same time, I want to know how they may lead to observable consequences in cosmological observations. In the long run, hopefully, we can uncover the 95% dark side of the Universe.
