Numerical Inflation

For my final project for my cosmology class, I numerically investigated single-field scalar inflation. The potential I used, quadratic inflation, has been ruled out by Planck but it was still nice to do the calculations of the spectral index and tensor-to-scalar ratio and see I get the same results. I then used Monte Carlo to show how non-Gaussianities arise from inflation and why they’re so hard to find. I’d like to extend this project to investigate eternal inflation, but that’s for the future. You can find my paper here (the code is TeXed in).

Asymptotic Freedom and the Background Field Method

I presented a group talk for my QFT II class on Peskin and Schroeder section 16.6, explaining the background field method and using it to derive the QCD beta function. I found the section in P&S to be utterly incomprehensible–they don’t really give you any clues to what they’re doing or how anything is defined or what is actually going on. Hopefully the attached notes go some way towards a decent explanation of the background field method. I found Schwartz’s QFT textbook to be much better on this point if you want to read more.

The Extended Press-Schechter Formalism

I gave a talk at the UM HET journal club on the Extended Press-Schechter formalism, which describes the number density distribution of halos (galaxy clusters) in ΛCDM. It starts from basic cosmology but assumes some results from inflationary theory without demonstration. The Press-Schechter formalism was a mildly accurate formalism with some problems; these problems are resolved in the extended formalism. Thanks to Dragan Huterer, my cosmology professor, for notes and to the very clear textbook MBW. You can access the lecture notes here.

The Higgs Mechanism

I gave a presentation in PHYS 510 Statistical Mechanics on the phase transition aspects of the Higgs Mechanism. It’s at a pretty basic level and anyone with a bit of quantum field theory knowledge should be able to follow. The slides are here.