A measure of gravitational entropy and structure formation

TL;DR

This paper proposes a quantization rule for gravitational entropy increase during structure formation, linking inhomogeneity growth to a discrete spectrum of cosmic structures and the arrow of time.

Contribution

It introduces a novel quantization framework for gravitational entropy, connecting inhomogeneity scales to a natural extremal condition during structure formation.

Findings

Discrete spectrum of nested cosmic structures derived

Gravitational entropy increase follows a quantized pattern

Arrow of time aligns with stepwise entropy growth

Abstract

Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is subject to a specific quantization rule for the amount of increase of gravitational entropy during the formation of inhomogeneities. The gain of gravitational entropy at each higher order merging process within the system is shown to result as a natural consequence from an extremal condition involved. The resulting discrete spectrum of nested, bound structures of specific mass and radius, ranging from the particle physics scale to galaxies and super clusters, provides a unified view of fundamental inhomogeneity scales in the universe from gravitational entropy considerations. Consequently, also the gravitational arrow of time points in the direction of stepwise increasing entropy or inhomogeneity, respectively.