Evolution of Cyclic Mixmaster Universes with Non-comoving Radiation

TL;DR

This paper investigates the evolution of cyclic, anisotropic mixmaster universes with non-comoving radiation, analyzing how entropy, cosmological constants, and velocity oscillations influence their dynamics and approach to flatness or isotropy.

Contribution

It introduces a combined numerical and analytic study of non-comoving radiation in Bianchi IX universes, revealing effects of entropy and cosmological constants on their cyclic evolution.

Findings

Entropy increases lead to larger volume maxima and greater anisotropy.

Velocities oscillate rapidly and change logarithmically with volume.

Positive cosmological constant promotes isotropisation and eternal expansion.

Abstract

We study a model of a cyclic, spatially homogeneous, anisotropic 'mixmaster' universe of Bianchi type IX, containing a radiation field with non-comoving ('tilted' with respect to the tetrad frame of reference) velocities and vorticity. We employ a combination of numerical and approximate analytic methods to investigate the consequences of the second law of thermodynamics on the evolution. We model a smooth cycle-to-cycle evolution of the mixmaster universe, bouncing at a finite minimum, by the device of adding a comoving 'ghost' field with negative energy density. In the absence of a cosmological constant, an increase in entropy, injected at the start of each cycle, causes an increase in the volume maxima, increasing approach to flatness, falling velocities and vorticities, and growing anisotropy at the expansion maxima of successive cycles. We find that the velocities oscillate rapidly as they evolve and change logarithmically in time relative to the expansion volume. When the conservation of momentum and angular momentum constraints are imposed, the spatial components of these velocities fall to smaller values when the entropy density increases, and vice versa. Isotropisation is found to occur when a positive cosmological constant is added because the sequence of oscillations ends and the dynamics expand forever, evolving towards a quasi de Sitter asymptote with constant velocity amplitudes. The case of a single cycle of evolution with a negative cosmological constant added is also studied.