Statistical Mechanics of gravitating systems in static and cosmological backgrounds

TL;DR

This review explores the statistical mechanics of gravitating systems in static and expanding backgrounds, emphasizing gravitational clustering, power spectrum evolution, and universal features in cosmological contexts.

Contribution

It provides a comprehensive overview of recent progress in understanding gravitational clustering and statistical properties in expanding universes, connecting concepts across physics disciplines.

Findings

Analysis of power transfer across scales in expanding backgrounds

Asymptotic behavior of density fluctuation spectra

Identification of universal clustering characteristics

Abstract

This pedagogical review addresses several issues related to statistical description of gravitating systems in both static and expanding backgrounds, focusing on the latter. After briefly reviewing the results for the static background, I describe the key issues and recent progress in the context of gravitational clustering of collision-less particles in an expanding universe. The questions addressed include: (a) How does the power injected into the system at a given wave number spread to smaller and larger scales? (b) How does the power spectrum of density fluctuations behave asymptotically at late times? (c) What are the universal characteristics of gravitational clustering that are independent of the initial conditions and manifest at the late time evolution of the system? The review is intended for non cosmologists and will be of interest to people working in fluid mechanics, non linear dynamics and condensed matter physics.