Matthew Reinhard - Computing the Trispectrum in Axion Inflation: Reduction to Low-D Integrals

Abstract: Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have found tentative evidence of parity violation in the Large-Scale Structure (LSS) of our Universe. If these measurements turn out to be correct, this discovery would have profound implications for fundamental physics. The forces involved in galaxy formation and evolution are known to be parity-symmetric, thus any new parity-violating interaction very likely came from the very earliest moments of the Universe, during inflation. We consider an inflationary model known as "axion inflation", with the axion itself driving the expansion of space. This model also includes a (parity-violating) Chern-Simons interaction between the axion and a U(1) gauge field. Computing the lowest order parity-sensitive statistic, the trispectrum, has proven to be a difficult task due to the presence of high-dimensional loop integrals. We have developed an analytical method which drastically reduces the dimensionality of these integrals from 16-D to, at worst, 6-D. This substantial simplification enables efficient numerical computation of the trispectrum, which will allow us to explore a wide range of the parameter space of wave vector configurations.