My Master’s degree project is about investigating the Large Scale Structures of the universe in redshift space and TDA is its tool.
Here you can find abstract of my project proposal:
Studying the large-scale structures of the universe provides us important information about the evolution of the cosmos as well as fundamental theories of the initial conditions. The diverse observable features of this field, along with various programs for observing and collecting them, in addition to various simulation methods, provide motivations to use tools such as mapping to complex networks called cosmic webs and algebraic topology. Utilizing these tools can lead to at least the following advantages:
- Eliminating existing uncertainties in the predictions of various cosmological models.
- Introducing observables independent of the new model.
Topology-based analysis and stable homology analysis of Betti numbers lead to more information compared to Euler characteristics and Genus topology and Minkowski functionals. In this study, based on topology-based analysis and specifically using persistent homology, we aim to determine the topological properties of observable structures of large-scale structures in the redshift space. We investigate the effect of peculiar velocity on the persistent homology of large-scale structures in both linear and nonlinear scales. We also intend to obtain constraints on cosmological quantities like Sigma_8 by analyzing the Fisher matrix. This study can serve as a prerequisite for studying and distinguishing between different cosmological models such as the standard model of cosmology and modified gravity models.