标题： 全宇称破坏三阶谱在轴子暴胀中的研究：降低到低维积分 显示英文标题

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

摘要： 最近对星系四点关联函数（4PCF）的测量似乎在高显著性水平上检测到了非零的宇称奇模式。 由于引力是星系形成和演化的主要驱动因素，它是宇称偶的，因此如果宇称破坏是真实的，很可能是早期宇宙中某种新的宇称破坏机制产生的。 在这里，我们研究了一个具有轴子和$U(1)$规范场之间陈-西蒙斯相互作用的暴胀模型，其中轴子本身是暴胀场。 评估原初曲率扰动的四谱（4PCF的傅里叶空间类比）是一个涉及非常高维环积分的复杂计算。 我们展示了如何通过将积分简化为卷积并利用卷积定理来简化这些积分，并执行所有角度积分的解析计算。 这使我们剩下低维径向积分，这些积分更容易进行高效的数值计算。 本文是系列论文的第一篇，我们将使用这些结果计算轴子暴胀的完整晚期4PCF，从而使得来自即将到来的三维光谱调查（如暗能量光谱仪器(DESI)、欧几里得或罗曼）的约束成为可能。 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.