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

研究启动奖为传统黑人学院和大学的初级和中期职业教师提供支持，他们正在建立新的研究项目或重新指导和重建现有的研究项目。期望该奖项有助于提高教师的研究能力和效率，改善所在机构的研究和教学，并使本科生参与研究经验。北卡罗来纳中央大学（North Carolina Central University）获得的这一奖项可能在许多领域产生更广泛的影响。该项目的目标是发展一种形式体系，用于研究早期宇宙中几何结构形成的种子，这与宇宙学研究中典型的假设不同。本科生参与了这项研究，该项目与许多其他机构合作。该项目旨在为传统Lambda冷暗物质（Lambda冷暗物质）范式的以下几何扩展开发一种全尺度宇宙摄动理论，旨在揭示宇宙的形状和体积：各向异性空间拓扑模型和非零空间曲率模型。这个理论将允许考虑物质密度的非线性对比。因此，它将适用于在任意亚视界和超视界距离上的宇宙结构生长的高精度模拟，以及宇宙逆反应效应的估计。我们将以弱场极限为基础，详细阐述所期望的形式，并采用离散宇宙学的方法，特别是将非相对论性物质以具有相应能量-动量张量的独立点状粒子的形式表示，并结合宇宙筛选方法。在所选模型中对非均匀宇宙中引力相互作用的全尺度描述将有助于区分相互竞争的场景、LambdaCDM范式及其替代方案，加深我们对宇宙拓扑结构的理解，并构建满足当前和未来高精度观测数据的高级模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.