The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as the power spectrum) to higher-order correlations. Moreover, information about the primordial non-Gaussian signal lies also in higher-order correlations. Without tapping into these, that information remains hidden. While the three-point function (or the bispectrum), even if not extensively, has been studied and applied to data, there has been only limited discussion about the four point/trispectrum. This is because the high-dimensionality of the statistics (in real space a skew-quadrilateral has 6 degrees of freedom), and the high number of skew-quadrilaterals, make the trispectrum numerically and algorithmically very challenging. Here we address this challenge by introducing the i-trispectrum, an integrated trispectrum that only depends on four $k$-modes moduli. We model and measure the matter i-trispectrum from a set of 5000 \textsc{Quijote} N-body simulations both in real and redshift space, finding good agreement between simulations outputs and model up to mildly non-linear scales. Using the power spectrum, bispectrum and i-trispectrum joint data-vector covariance matrix estimated from the simulations, we begin to quantify the added-value provided by the i-trispectrum. In particular, we forecast the i-trispectrum improvements on constraints on the local primordial non-Gaussianity amplitude parameters $f_\mathrm{nl}$ and $g_\mathrm{nl}$. For example, using the full joint data-vector, we forecast $f_\mathrm{nl}$ constraints up to two times ($\sim32\%$) smaller in real (redshift) space than those obtained without i-trispectrum.

中文翻译：

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物质三谱：理论建模和与 N 体模拟的比较

长期以来，功率谱一直是大规模结构宇宙学分析的主要汇总统计数据。然而，引力非线性演化将宝贵的宇宙学信息从两点统计（如功率谱）转移到高阶相关性。此外，关于原始非高斯信号的信息也存在于高阶相关性中。如果不利用这些信息，这些信息就会被隐藏起来。虽然三点函数（或双谱），即使没有被广泛研究并应用于数据，但关于四点/三谱的讨论也很有限。这是因为统计量的高维（在真实空间中斜四边形有 6 个自由度），以及大量的斜四边形，使三谱在数值和算法上非常具有挑战性。在这里，我们通过引入 i-trispectrum 来解决这一挑战，这是一个仅依赖于四个 $k$-modes 模的集成三谱。我们在真实空间和红移空间中从一组 5000 个 \textsc{Quijote} N 体模拟中建模和测量物质 i-三谱，在模拟输出和模型之间找到了很好的一致性，直到温和的非线性尺度。使用从模拟中估计的功率谱、双谱和 i-trispectrum 联合数据向量协方差矩阵，我们开始量化 i-trispectrum 提供的附加值。特别是，我们预测了对局部原始非高斯幅度参数 $f_\mathrm{nl}$ 和 $g_\mathrm{nl}$ 的约束的 i-trispectrum 改进。例如，使用全关节数据向量，