April 21, 2021

Persistent homology of the cosmic web – From dark matter density fields, halos and (at some point) observations

Georg Wilding, University of Groningen

Abstract:

The structure of the cosmic web, its connectivity and multiscale, geometric nature, has been of the centre of extensive research in the past decades. We study the underlying dark matter distribution in LCDM using persistent homology. It provides information on characteristic densities of topological features, their hierarchical interactions, multiscale connectivity and percolation. With elements of homology theory, such as Betti numbers to count holes of various dimensions, we trace the evolution of the hierarchical structure, geometry and connectivity of the cosmic web in a set of cosmological N-body simulations. Within homology theory, persistence quantifies the longevity and stability of topological features. Features with high persistence can be associated with the prominent structural components in the multicomponent, multidimensional cosmic web. Together with another homological feature, the Betti curves, this concisely and richly describes the evolution of the topological shape of the cosmic web. Taking a step back, we then use this information to discern differences in the cosmic web topology between various dark energy cosmologies, as well as to identify a topological bias in the DM halo distribution.

Recorded video for the talk (click)