标题： 轴子暴胀中的完全宇称破坏三功率谱：约化为低维积分 显示英文标题

标题： Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals

摘要： 近期对星系四点关联函数（4PCF）的测量似乎在高显著性下检测到了非零的宇称奇性模式。 由于引力——星系形成和演化的主导力量是宇称偶性的，因此如果存在任何真实的宇称破缺，则很可能是早期宇宙中某种新的宇称破缺机制产生的。 在这里我们研究了一个暴胀模型，其中轴子与一个 $U(1)$规范场之间存在陈-西蒙斯相互作用，其中轴子本身是暴胀场。 计算原初曲率扰动的四点谱（4PCF的傅里叶空间类比）是一项复杂的计算，涉及非常高维的环路积分。 我们展示了如何简化这些积分，并通过将积分约化为卷积并利用卷积定理来解析地完成所有角积分。 这使我们得到了低维的径向积分，这些积分更容易进行高效的数值评估。 本文是系列文章的第一篇，在这一系列文章中，我们将利用这些结果计算轴子暴胀的完整晚期4PCF，从而能够从即将进行的三维光谱巡天（如暗能量光谱仪（DESI）、欧几里得或罗马任务）中得出限制。 显示英文摘要

摘要： Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have seemingly detected non-zero parity-odd modes at high significance. Since gravity, the primary driver of galaxy formation and evolution is parity-even, any parity violation, if genuine, is likely to have been produced by some new parity-violating mechanism in the early Universe. Here we investigate an inflationary model with a Chern-Simons interaction between an axion and a $U(1)$ gauge field, where the axion itself is the inflaton field. Evaluating the trispectrum (Fourier-space analog of the 4PCF) of the primordial curvature perturbations is an involved calculation with very high-dimensional loop integrals. We demonstrate how to simplify these integrals and perform all angular integrations analytically by reducing the integrals to convolutions and exploiting the Convolution Theorem. This leaves us with low-dimensional radial integrals that are much more amenable to efficient numerical evaluation. This paper is the first in a series in which we will use these results to compute the full late-time 4PCF for axion inflation, thence enabling constraints from upcoming 3D spectroscopic surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, or Roman.