  In this research, we investigate the structural evolution of the cosmic web,
employing advanced methodologies from Topological Data Analysis. Our approach
involves leveraging LITE, an innovative method from recent literature that
embeds persistence diagrams into elements of vector spaces. Utilizing this
methodology, we analyze three quintessential cosmic structures: clusters,
filaments, and voids. A central discovery is the correlation between
\textit{Persistence Energy} and redshift values, linking persistent homology
with cosmic evolution and providing insights into the dynamics of cosmic
structures.
