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

研究启动奖为历史上黑人学院和大学的初级和中级职业教师提供支持，他们正在建立新的研究项目或重新定向和重建现有的研究项目。预计该奖项将有助于进一步提高教师的研究能力和效率，改善家庭机构的研究和教学，并使本科生参与研究经验。授予北卡罗来纳州中央大学的奖项在许多领域都有潜在的更广泛的影响。该项目的目标是开发一种形式主义，用于研究早期宇宙中结构形成的种子，其几何形状不同于宇宙学研究中通常假设的几何形状。 本科生参与了这项研究，该项目与其他一些机构合作。该项目旨在为传统的Lambda冷暗物质（Lambda cold dark matter）范式的以下几何扩展开发一个全尺度宇宙学微扰理论，旨在揭示宇宙的形状和体积：具有各向异性空间拓扑结构的模型和具有非零空间曲率的模型。这个理论将允许考虑物质密度的非线性对比。因此，它将适用于高精度的模拟宇宙结构的增长在任意的亚视界和超视界的距离，以及宇宙学的反反应效应的估计。所需形式的验证将基于弱场极限，离散宇宙学的方法，特别是将非相对论性物质以独立的点状粒子的形式呈现，并具有相应的能量-动量张量，结合宇宙屏蔽方法。在选定的模型中，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竞争场景，LambdaCDM范式及其替代方案，加深我们对宇宙拓扑结构的理解，建立了一个满足当前和未来高精度数据的先进模型，该奖项反映了NSF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.