Title: Two is better than one: joint statistics of density and velocity in concentric spheres as a cosmological probe Show Chinese title

Title: 两个优于一个：同心球体中密度和速度联合统计作为宇宙学探针

Abstract: The analytical formalism to obtain the probability distribution functions (PDFs) of spherically-averaged cosmic densities and velocity divergences in the mildly non-linear regime is presented. A large-deviation principle is applied to those cosmic fields assuming their most likely dynamics in spheres is set by the spherical collapse model. We validate our analytical results using state-of-the-art dark matter simulations with a phase-space resolved velocity field finding a 2% percent level agreement for a wide range of velocity divergences and densities in the mildly nonlinear regime (~10Mpc/h at redshift zero), usually inaccessible to perturbation theory. From the joint PDF of densities and velocity divergences measured in two concentric spheres, we extract with the same accuracy velocity profiles and conditional velocity PDF subject to a given over/under-density which are of interest to understand the non-linear evolution of velocity flows. Both PDFs are used to build a simple but accurate maximum likelihood estimators for the redshift evolution of the variance of both the density and velocity divergence fields, which have smaller relative errors than their sample variances when non-linearities appear. Given the dependence of the velocity divergence on the growth rate, there is a significant gain in using the full knowledge of both PDFs to derive constraints on the equation of state of dark energy. Thanks to the insensitivity of the velocity divergence to bias, its PDF can be used to obtain unbiased constraints on the growth of structures ($\sigma_8$,f) or it can be combined with the galaxy density PDF to extract bias parameters. Show Chinese abstract

Abstract: 获得在弱非线性 regime 中球对称平均宇宙密度和速度散度的概率分布函数（PDFs）的分析形式主义被提出。应用大偏差原理于这些宇宙场，假设其最可能的动力学由球形坍缩模型决定。我们使用最先进的暗物质模拟验证了分析结果，这些模拟具有相空间分辨的速度场，在弱非线性 regime 中（红移为零时约 10Mpc/h），对于广泛的速度散度和密度，达到了 2% 的精度，通常无法通过微扰理论获得。从两个同心球中测量到的密度和速度散度的联合 PDF 中，以相同的精度提取出速度剖面和给定过/欠密度条件下的速度 PDF，这对于理解速度流的非线性演化具有重要意义。这两个 PDF 被用来构建简单的但准确的最大似然估计器，用于红移演化中的密度和速度散度场方差，当出现非线性时，它们的相对误差比样本方差更小。鉴于速度散度依赖于增长速率，利用两个 PDF 的全部知识来推导暗能量状态方程的约束会有显著提升。由于速度散度对偏差不敏感，其 PDF 可用于获得对结构增长（$\sigma_8$,f）的无偏约束，或者可以与星系密度 PDF 结合以提取偏差参数。