Weak lensing probes of primordial non-Gaussianity and mass estimators of weak-lensing clusters

弱引力透镜（WL）是确定描述宇宙的宇宙学参数的主要工具之一。特别是，它可以测量暗能量的状态方程，也可以用来检验广义相对论。这一建议提出了两条调查路线，考虑到即将进行的短期和长期透镜调查，这两条路线特别有用。第一行论述了WL调查测量原始非高斯性的潜力。我们将使用费雪矩阵形式来确定哪些WL可观测值适合于这项任务。然后，这些观测结果将在通过射线追踪通过结构形成的数值模拟获得的剪切图中进行测量。模拟是“最先进的”，并且已经在高斯和非高斯初始条件下发展。因此，可以用数值方法探测WL观测值对原始非高斯性的敏感性。将测试和组合的观测值包括剪切峰、剪切功率谱和剪切双谱。这项研究在几个方面是创新的，应该会产生对未来调查有用的结果。研究的第二条线是对剪切峰所携带的宇宙学信息的全面探索。由于宇宙学的限制，剪切峰的2点和3点相关函数以及剪切峰与剪切场的相互关系尚未得到探索。我们将从理论上和在WL图中研究它们，并将评估它们对原始非高斯性的敏感性。另一个主要目标是给出剪切峰函数的理论预测，也得到数值测量的支持。

Weak gravitational lensing (WL) is one of the prime tools to determine the cosmological parameters describing the universe. In particular, it can measure the equation of state of Dark Energy, and it can also be used to test General Relativity. This proposal suggests two lines of investigation, particularly useful in view of the short- and long-term upcoming lensing surveys. The first line addresses the potential of WL surveys to measure primordial non-Gaussianity. We shall use the Fisher matrix formalism to establish which WL observables are suited for this task. These observables will then be measured in shear maps obtained by ray-tracing through numerical simulations of structure formation. The simulations are ‘state-of-the-art’ and have been evolved with both Gaussian and non-Gaussian initial conditions. Thus, it will be possible to probe numerically the sensitivity of WL observables to primordial non-Gaussianity. Among the observables that will be tested and combined are shear peaks, the shear power spectrum, and the shear bispectrum. This study is innovative on several counts, and should yield results that will be useful for future surveys.The second line of research is a full exploration of the cosmological information carried by shear peaks. The 2- and 3-point correlation functions of the shear peaks, as well as the cross-correlation of shear peaks and the shear field have not yet been explored for cosmological constraints. We shall study them both theoretically and in WL maps, and we shall also assess their sensitivity to primordial non-Gaussianity. The other major goal is to give a theoretical prediction for the shear-peak function, also backed up by numerical measurements.