Approaching Wonderland

TL;DR

This paper investigates the asymptotic behavior of certain Bianchi cosmological models with p-form fields and perfect fluids, identifying stable attractors called Wonderland and others across various invariant sets.

Contribution

It extends previous work by analyzing new Bianchi invariant sets and discovering the Wonderland attractor's stability in these models, along with new gravitational wave solutions.

Findings

Wonderland is a future attractor for 2/3<γ<2 in most sets.

Edge and Rope equilibria dominate in Bianchi II for certain γ.

Gravitational wave solutions serve as attractors in some models.

Abstract

Continuing previous work, we show the existence of stable, anisotropic future attractors in Bianchi invariant sets with a $p$-form field ($p\,\in\,\{1,3\}$) and a perfect fluid. In particular, we consider the not previously investigated Bianchi invariant sets $\mathcal{B}$(II), $\mathcal{B}$(IV), $\mathcal{B}$(VII$_0$) and $\mathcal{B}$(VII$_{h})$ and examine their asymptotic behaviour. We find that the isolated equilibrium set Wonderland is a future attractor on all of its existence ($2/3<\,\gamma\,<2$) in all these sets except in $\mathcal{B}$(II), where the peculiar equilibrium sets Edge and Rope show up, taking over the stability for certain values of $\gamma$. In addition, in $\mathcal{B}$(IV) and $\mathcal{B}$(VII$_h$) plane gravitational wave solutions (with a non-zero $p$-form) serve as attractors whenever $2/3<\,\gamma\,<2$.