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GR: Fachverband Gravitation und Relativitätstheorie

GR 10: Cosmo II

GR 10.2: Vortrag

Donnerstag, 3. April 2025, 14:15–14:35, ZHG008

Betti Functionals as Probes for Cosmic Topology — Ralf Aurich and •Frank Steiner — Institute for Theoretical Physics, Ulm University, Albert-Einstein-Alle 11,89060 Ulm

The question of the global topology of the Universe (cosmic topology) is still open. In the LCDM concordance model,it is assumed that the space of the Universe possesses the trivial topology of R^3, and thus that the Universe has an infinite volume. We study one of the simplest non-trivial topologies given by a cubic 3-torus describing a universe with a finite volume. To probe cosmic topology, we analyze certain structures in the cosmic microwave background (CMB) using Betti functionals and the Euler characteristic evaluated on excursion sets, which possess a simple geometrical interpretation. Since the CMB temperature fluctuations are observed on the sphere S^2 surrounding the observer, there are only 3 Betti functionals, beta_k(nu), k=0,1,2 (nu is the temperature threshold). Analytic approximations of the Gaussian expectations for the Betti functionals and an exact formula for the Euler characteristic are given. It is shown that beta_0 and beta_1 decrease with an increasing volume of the cubic 3-torus universe. Comparing with 4 Planck 2018 sky maps, it is found that the betas of the Planck maps lie between those of the torus universes with side-lengths L=2.0 and L=3.0 in units of the Hubble length. These results give a further hint that the Universe has a non-trivial topology. Ref.: Universe 2024, 10, 190

Keywords: Relativistische Astrophysik; Allgemeine Relativitaetstheorie; Experimentelle Tests