Points The universe seems to be ±lled with a mysterious...

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Physics 253a: Quantum Field Theory I Prof. Schwartz Due Friday December 14 by 12pm. Final Exam 2018 Please answer the following questions and return the solutions either online or to Ho±e by 5pm December 14. You can use the textbook/lecture notes, problem set solutions, and Mathematica or its equivalents if you need help with the math. Do not use any other resources, including any other textbook, your peers, or the web. Do not use any mathematica package other than the built- in functions. You are expected to do this exam entirely on your own. 1. (40 points) The universe seems to be ±lled with a mysterious substance called ²dark matter³, which appears to interact gravitationally, with a density of about 0.3 GeV/cm 3 . Since we cannot see the dark matter, it cannot have electric charge. On the other hand, it must have some non-gravitational interactions to match our models of early universe cosmology. The leading candidates for what dark matter might be are Weakly Interacting Massive Particles, or WIMPs which could interact with matter only through the weak force. Such

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