Research Initiation Award: Effect of the Universe Topology on Cosmological Perturbations

研究启动奖为历史悠久的黑人学院和大学的初级和职业生涯中期教师提供支持，这些教师正在建立新的研究计划或重新定向和重建现有的研究计划。预计该奖项有助于进一步提高教师的研究能力和有效性，改善所在机构的研究和教学，并让本科生参与研究经验。授予北卡罗来纳中央大学的奖项可能在许多领域产生更广泛的影响。这个项目的目标是发展一种形式主义，以不同于宇宙学研究中通常假设的几何形式来研究早期宇宙中结构形成的种子。本科生参与了这项研究，该项目与其他一些机构也有合作。该项目旨在发展一个全尺度的宇宙学微扰理论，用于对传统的LambdaCDM(Lambda冷暗物质)范例的几何扩展，旨在揭示宇宙的形状和体积：具有各向异性空间拓扑的模型和具有非零空间曲率的模型。这一理论将允许考虑物质密度的非线性对比。因此，它将适用于任意亚视界和超视界距离处的宇宙结构生长的高精度模拟，以及对宇宙学反向反应效应的估计。所需形式的阐述将基于弱场极限，并将使用离散宇宙学的方法，特别是将非相对论物质表示为具有相应能量动量张量的单独的点状粒子的形式，并结合宇宙筛选方法。在选定的模型中，对非均匀宇宙中引力相互作用的全方位描述将有助于区分相互竞争的场景、LambdaCDM范例及其替代方案，加深我们对宇宙拓扑的理解，并构建满足当前和未来高精度观测数据的高级模型。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to North Carolina Central University has potential broader impacts in a number of areas. The goal of this project is to develop a formalism for studying the seeds of structure formation in the early universe in geometries that are different from those that are typically assumed in cosmological research. Undergraduate students are involved in this research and the project has collaborations with a number of other institutions. The project seeks to develop an all-scale cosmological perturbation theory for the following geometrical extensions of the conventional LambdaCDM (Lambda cold dark matter) paradigm, which aim at revealing the shape and volume of the universe: models with anisotropic spatial topologies and models with nonzero spatial curvature. This theory will permit consideration of nonlinear contrasts of the matter density. Thus, it will be suitable for high-precision simulations of the cosmic structure growth at arbitrary - sub-horizon and super-horizon - distances, as well as for the estimation of the cosmological backreaction effects. Elaboration of the desired formalism will be based on the weak field limit, and methods of discrete cosmology, particularly the presentation of nonrelativistic matter in the form of separate point-like particles with the corresponding energy-momentum tensor, in combination with the cosmic screening approach will be employed. The all-scale description of the gravitational interaction in the inhomogeneous universe within the selected models will assist in distinguishing among the competing scenarios, the LambdaCDM paradigm and its alternatives, deepening of our understanding of the universe topology, and constructing an advanced model satisfying the data of present and future high-precision observations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.