In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected matter density field and more specifically to the angular aperture masses. The latter holds the advantage of being an observable that can be directly extracted from the observed shear field and to be, by construction, independent from the long wave modes. Furthermore, we show that, with the help of a nulling procedure based on the so-called BNT transform, it is possible to build observables that depend only on a finite range of redshifts making them also independent from the small-scale modes. This procedure makes predictions for the shape of the one-point probability distribution function of such an observable very accurate, comparable to what had been previously obtained for 3D observables. Comparisons with specific simulations reveal however inconsistent results showing that synthetic lensing maps were not accurate enough for such refined observables. It points to the need for more precise dedicated numerical developments whose performances could be benchmarked with such observables. We furthermore review the possible systematics that could affect such a formalism in future weak-lensing surveys like Euclid, notably the impact of shape noise as well as leading corrections coming from lend–lens couplings, geodesic deviation, reduced shear and magnification bias.

中文翻译：

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大偏差理论的孔径质量场概率分布函数

在断层宇宙切变测量的背景下，开发了孔径质量（地图）单点统计的理论模型。这种形式是基于将大偏差原理应用于投影物质密度场，更具体地说是应用于角孔径质量。后者的优点是可以直接从观察到的剪切场中提取出可观察的，并且通过构造独立于长波模式。此外，我们表明，借助基于所谓 BNT 变换的归零程序，可以构建仅依赖于有限范围的红移的可观察量，从而使其也独立于小尺度模式。这个过程使得对这种可观测的单点概率分布函数的形状的预测非常准确，与之前获得的 3D 可观测的结果相媲美。然而，与特定模拟的比较揭示了不一致的结果，表明合成透镜图对于如此精细的可观测物来说不够准确。它指出需要更精确的专用数值开发，其性能可以用这些可观察的作为基准。我们进一步回顾了可能影响未来弱透镜测量（如欧几里得）中这种形式主义的可能系统学，特别是形状噪声的影响以及来自借透镜耦合、测地线偏差、减少的剪切和放大偏差的领先校正的影响。与之前获得的 3D 可观测值相当。然而，与特定模拟的比较揭示了不一致的结果，表明合成透镜图对于如此精细的可观测物来说不够准确。它指出需要更精确的专用数值开发，其性能可以用这些可观察的作为基准。我们进一步回顾了可能影响未来弱透镜测量（如欧几里得）中这种形式主义的可能系统学，特别是形状噪声的影响以及来自借透镜耦合、测地线偏差、减少的剪切和放大偏差的领先校正的影响。与之前获得的 3D 可观测值相当。然而，与特定模拟的比较揭示了不一致的结果，表明合成透镜图对于如此精细的可观测物来说不够准确。它指出需要更精确的专用数值开发，其性能可以用这些可观察的作为基准。我们进一步回顾了可能影响未来弱透镜测量（如欧几里得）中这种形式主义的可能系统学，特别是形状噪声的影响以及来自借透镜耦合、测地线偏差、减少的剪切和放大偏差的领先校正的影响。它指出需要更精确的专用数值开发，其性能可以用这些可观察的作为基准。我们进一步回顾了可能影响未来弱透镜测量（如欧几里得）中这种形式主义的可能系统学，特别是形状噪声的影响以及来自借透镜耦合、测地线偏差、减少的剪切和放大偏差的领先校正的影响。它指出需要更精确的专用数值开发，其性能可以用这些可观察的作为基准。我们进一步回顾了可能影响未来弱透镜测量（如欧几里得）中这种形式主义的可能系统学，特别是形状噪声的影响以及来自借透镜耦合、测地线偏差、减少的剪切和放大偏差的领先校正的影响。