# The Geometry and Topology of the Cosmic Web

Monday, October 7, 2013 - 11:30am - 12:20pm

Keller 3-180

Rien van de Weijgaert (Rijksuniversiteit te Groningen)

The Cosmic Web is the fundamental spatial organization of matter on scales of a few up to a hundred

Megaparsec, scales at which the Universe still resides in a state of moderate dynamical evolution.

galaxies, intergalactic gas and dark matter exist in a wispy weblike spatial arrangement consisting of

dense compact clusters, elongated filaments, and sheetlike walls, amidst large near-empty void regions.

While the complex intricate structure of the cosmic web contains a wealth of cosmological

information, its quantification has remained a major challenge. In this lecture, we describe

recent work towards invoking concepts from computational topology and computational

geometry to our understanding of the structure of the Cosmic Web and to new insights into

the conditions in the primordial Universe out of which it emerged.

An important aspect of our understanding of the Cosmic Web concerns the connectivity

of the various components. This leads us to recent work on the topological analysis

of the Megaparsec scale distribution. To this end, we resort to the homology of the

weblike structure, and determine the scale-dependent Betti numbers. To infer this from the discrete

spatial galaxy distribution (or of particles in computer models of cosmic structure formation)

we extract the Betti numbers from alpha shapes. We have studied the alpha complex of the cosmic weblike

point patterns, in order to assess the signature of filaments, walls and voids. Of considerable

importance within the context of the multiscale nature of the cosmic mass distrbution, is the

information contained in persistence diagrams. Amongst others, I will describe recent work on

persistence properties of Gaussian and non-Gaussian random density fields, which form the initial

conditions out of which the cosmic web emerged through the force of gravity.

Megaparsec, scales at which the Universe still resides in a state of moderate dynamical evolution.

galaxies, intergalactic gas and dark matter exist in a wispy weblike spatial arrangement consisting of

dense compact clusters, elongated filaments, and sheetlike walls, amidst large near-empty void regions.

While the complex intricate structure of the cosmic web contains a wealth of cosmological

information, its quantification has remained a major challenge. In this lecture, we describe

recent work towards invoking concepts from computational topology and computational

geometry to our understanding of the structure of the Cosmic Web and to new insights into

the conditions in the primordial Universe out of which it emerged.

An important aspect of our understanding of the Cosmic Web concerns the connectivity

of the various components. This leads us to recent work on the topological analysis

of the Megaparsec scale distribution. To this end, we resort to the homology of the

weblike structure, and determine the scale-dependent Betti numbers. To infer this from the discrete

spatial galaxy distribution (or of particles in computer models of cosmic structure formation)

we extract the Betti numbers from alpha shapes. We have studied the alpha complex of the cosmic weblike

point patterns, in order to assess the signature of filaments, walls and voids. Of considerable

importance within the context of the multiscale nature of the cosmic mass distrbution, is the

information contained in persistence diagrams. Amongst others, I will describe recent work on

persistence properties of Gaussian and non-Gaussian random density fields, which form the initial

conditions out of which the cosmic web emerged through the force of gravity.

MSC Code:

54E20

Keywords: