AI 中文总结
该研究将弱引力透镜汇聚三谱作为晚期大尺度结构宇宙学宇称破缺的探测手段，推导投影形式，用模板计算宇称奇信号及信噪比，评估不同红移分布，绘制几何灵敏度，测试近似有效性，证明可利用弱引力透镜调查探测早期宇宙基本对称性。
AI 中文摘要
我们确立了弱引力透镜汇聚三谱作为晚期大尺度结构（LSS）中宇宙学宇称破缺的独立探测手段。为将三维原初对称性映射到二维可观测量，我们推导了适用于两类可分解原初曲率三谱的约化角三谱的广义紧凑投影形式。应用此框架，我们用两个唯象的宇称破缺三谱模板计算了宇称奇信号并预测了预期信噪比。分析评估了理想化的狄拉克δ源红移分布以及来自暗能量调查第3年（DES Y3）的实际层析剖面和时空遗产调查第10年（LSST Y10）的预测剖面。我们绘制了这些模板的几何灵敏度，揭示了信噪比如何受特定源星系红移分布和配置底层几何结构的强烈调制。此外，我们严格测试了高阶角统计中Limber近似的有效性，证明了精确视线数值积分以准确捕捉宇称破缺信号的必要性。通过展示通过弱引力透镜对宇称破缺特征的理论可探测性，这项工作提供了原理证明，表明即将进行的弱引力透镜调查可用于探测早期宇宙的基本对称性。
英文摘要
We establish the weak gravitational lensing convergence trispectrum as an independent probe of cosmological parity violation in the late-time Large-Scale Structure (LSS). To map three-dimensional primordial symmetries into two-dimensional observables, we derive a generalized, compact projection formalism for the reduced angular trispectrum applicable to two classes of factorizable primordial curvature trispectra considered in this work. Applying this framework, we compute the parity-odd signal and forecast the expected Signal-to-Noise Ratio (SNR) using two phenomenological parity-violating trispectrum templates. These two templates encode the initial conditions for the late-time weak lensing observables. One template peaks at the squeezed limit, and the other template peaks at the collapsed limit. Our analysis evaluates idealized Dirac-delta source redshift distributions alongside actual tomographic profiles from the Dark Energy Survey Year 3 (DES Y3) and forecasted profiles for the Legacy Survey of Space and Time Year 10 (LSST Y10). We map the geometric sensitivity of these templates, providing physical intuition into how the resulting SNR is strongly modulated by the specific source galaxy redshift distributions and the underlying geometry of the configurations. Furthermore, we rigorously test the validity of the Limber approximation for higher-order angular statistics, demonstrating the necessity of exact line-of-sight numerical integration to capture the parity-violating signal accurately. By demonstrating the theoretical detectability of parity-breaking signatures through weak lensing, this work serves as a proof of principle, showing how upcoming weak lensing surveys can be leveraged to probe the fundamental symmetries of the early universe.
Comments57 pages, 30 figures. Comments are welcome
