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

Title: 双倍胜过单个：同心球体中密度和速度的联合统计作为宇宙探测器

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: 提出了获取球平均宇宙密度和温和非线性态速度散度概率分布函数（PDF）的解析形式化方法。假设这些宇宙场在球内的最可能动力学由球坍缩模型决定，应用大偏差原理到这些宇宙场。我们利用最先进的相空间分辨速度场的暗物质模拟验证了我们的解析结果，在零红移约10Mpc/h的温和非线性态范围内（通常扰动理论难以触及），得到了约2%水平的符合度。从两个同心球测量的密度和速度散度联合PDF中，我们以相同的精度提取了速度剖面和给定过密/欠密条件下的速度PDF，这对理解速度流的非线性演化具有重要意义。这两个PDF被用来构建一个简单但准确的最大似然估计器，用于描述密度和速度散度场方差随红移演化的规律，当非线性出现时，其相对误差比样本方差更小。鉴于速度散度对增长率的依赖性，利用这两个PDF的完整知识来推导暗能量状态方程约束有显著优势。由于速度散度对偏倚不敏感，其PDF可用于获得无偏的结构增长约束（$\sigma_8$,f），也可以与星系密度PDF结合以提取偏倚参数。