Collins in Wonderland

Abstract

This paper is a continuation of our previous work on Bianchi cosmologies with a p-form field (where p ∈ {1, 3}) -or equivalently: an inhomogeneous, massless scalar gauge field with a homogeneous gradient. In this work we investigate such matter sector in General Relativity, and restrict to space-times of the particular Bianchi types VI 0 and VI h for h = −1/9 ∪ −1. Relying on our previous analysis, the aim of this paper is clean cut: We show that the versions of Wonderland found in B(VII 0 ) and B(VII h ) are both attractors. Also, we show that Wonderland is an extension of the previously found Collins equilibrium point. With this paper, our analysis of Bianchi space-times with a p-form field (p ∈ {1, 3}) is nearing an end. Only the special cases h = −1 and h = −1/9 are left for future work. The line-elements of the anisotropic attractors are also written down explicitly.

Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter

“…[12,14]), other matter models (e.g. [19,29] and references therein), and finally the collisionless kinetic gas which is the subject of the present work. On the observational level, however, it has been shown that Planck data do not favour the inclusion of a Bianchi type VII h component [24], although the observed large-scale intensity pattern mimics only that of the Bianchi type VII h because the Bianchi type VII h is the most general SH spacetime that contains flat and open FLRW models for h = 0 and h = 0, respectively.…”

Extended FLRW models: dynamical cancellation of cosmological anisotropies

“…To understand whether or not these principles are enforced by observational data, it is necessary to consider models that break at least some of them, and to test its observational consequences. To this end, a natural framework is provided by Bianchi models, which are spatially homogeneous cosmological models that may break three-dimensional (3D) rotational invariance in various ways: the fundamental congruence may possess shear [16][17][18][19][20][21] and vorticity [16,17,[22][23][24][25]; the matter sector may possess anisotropic stress [26][27][28][29][30][31][32][33][34][35][36][37][38] and tilt [39][40][41]; spatial sections of homogeneity may possess anisotropic curvature [19][20][21]42]. Note that the various types of anisotropies do not evolve independently but are intimately connected via Einstein's field equations.…”

Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter

“…[12,14]), other matter models (e.g. [19,29] and references therein), and finally the collisionless kinetic gas which is the subject of the present work. On the observational level, however, it has been shown that Planck data do not favour the inclusion of a Bianchi type VII h component [24].…”