Gravitational entropy and the cosmological no-hair conjecture

TL;DR

This paper investigates the apparent contradiction between gravitational entropy growth and the cosmological no-hair conjecture, using the Simsilun simulation based on the Silent Universe approximation, and finds that both conjectures hold true in a universe with dark energy.

Contribution

It demonstrates through simulation that gravitational entropy can grow while the universe approaches a de Sitter state, reconciling two seemingly contradictory conjectures.

Findings

Universe approaches de Sitter state asymptotically

Gravitational entropy continues to grow over time

Both conjectures are validated by simulation results

Abstract

The gravitational entropy and no-hair conjectures seems to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, non-viscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t = 25 Myr) till far future (t = 1000 Gyr). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and non-positive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy.