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GR: Fachverband Gravitation und Relativitätstheorie

GR 15: Cosmo III

GR 15.2: Vortrag

Freitag, 4. April 2025, 11:20–11:40, ZHG008

Velocity statistics of cosmic large-scale structure from Hamiltonian particle dynamics — •Marvin Sipp — Institut für Theoretische Physik, Universität Heidelberg, Deutschland

We present a novel approach to analytically calculating the evolution of velocity statistics of cosmic large-scale structure in cold dark matter.

It is based on a path-integral formulation for the Hamiltonian dynamics of an ensemble of classical particles, specialised to the self-gravitating case on an expanding background. Density and momentum statistics can be extracted by applying suitable operators to the generating functional. The full theory contains the complete phase-space information of the interacting particle ensemble. In practice, we solve the free theory and include interactions perturbatively, reminiscent of other statistical or quantum field theories. The theory can be reformulated in terms of macroscopic fields, leading to an efficient partial resummation of the microscopic perturbative series. Going to higher orders in this perturbation theory is equivalent to integrating higher moments of the BBGKY hierarchy. We thus avoid the shell-crossing problem of standard Eulerian perturbation theory (without introducing effective parameters), allowing for the generation of vorticity in initially irrotational systems and making our framework particularly interesting for studying the evolution of velocity statistics.

We show how n-point momentum statistics can be extracted from the free theory, how gravitational interactions can be included and partially resummed, and present the resulting two-point statistics of the momentum density and density-momentum cross-correlations.

Keywords: Large-Scale Structure; Field Theory; Statistical Mechanics; Gravitation; Perturbation Theory