Frozen Rigging Model of the Energy Dominated Universe

Abstract

Abstract. Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out into static lattice type configurations with energy contribution ultimately be provided by the membranes. It has been suggested by Bucher and Spergel that on scales large compared with the relevant (interstellar separation) distance characterising the relevant mesh length, such a system may behave as a rigidity -stabilised solid, having an approximately isotropic stress energy tensor with negative pressure, as given by a polytropic index γ = w + 1 = 1/3. It has recently been shown that such a system can be rigid enough to be stable if the number of membranes meeting at a junction is even (though not if it is odd). Using as examples an approximately O(3) symmetric scalar field model that can provide an "8 color" (body centered) cubic lattice, and an approximate U(1)× U(1) model offering a disordered "5 color" lattice, it is argued that such a mechanism can account naturally for the observed dark energy dominance of the universe, without ad hoc assumptions, other than that the relevant symmetry breaking phase transition should have occurred somewhere about the Kev energy range.

Defect junctions and domain wall dynamics

“…A very similar analogue was introduced by Carter in Ref. [23]. This indeed has five evenly spaced minima, and all the walls are of the same energy-the only difference is that Carter's model is of φ 4 type, while ours is of φ 6 type.…”

“…We provide a general and explicit construction of this ideal model, and again numerically study some examples. The pentahedral symmetry model discussed in [23] turns out to have some of these properties of this ideal model. In the interest of clarity, we shall start by discussing the simplest models, and gradually move on to more elaborate ones.…”

Stability of winding cosmic wall lattices with X type junctions

“…These values are comparatively small (not comparable, as was stated due to a transcription error) with respect to the interstellar distance scale, of the order of several parsecs, which is what would be obtained for ℓ c if one used the rather larger mass values m ⋆ ≈ η ≈ 10 −1 m e that were suggested by an analysis of the cruder kind used in earlier work [2]. However it now seems that all such reasoning, whether in its earlier form or in the more refined [6] version, should be considered to be effectively obsolete, because its generic outcome will be the formation of disorganised lattice configurations that would be insufficiently stable, unlike the superposed lasagne type configurations envisaged here. The whole question of the wall formation process needs to be entirely reconsidered in the context of the stabilisation mechanism considered here, which does not work for random wall lattice configurations, but is essentially dependent on the existence of effectively conserved winding numbers with sufficiently large values, representing the effect of systematic winding in the same sense over a cosmologically large scale.…”

“…1), a requirement that was not explicitly checked in the particular toy field models I suggested [6] as examples in my original discussion of this subject, and that has been called into doubt [9] in the particular case of what will be referred to here as the pentavac doublet model. In order to address the lattice stability question, a preliminary task of the present work will to provide a simple general criterion for the stability of such an X type equilibrium junction.…”

“…(Since they went so far as to claim that the viability of my proposed pentavac example [6] was "easily" ruled out by their numerical work, despite the fact that the latter was confined to a limited -apparently inappropriate -part of the relevant parameter space, the present article will therefore give particular attention to the provision of analytic reasonning showing that this pentavac model does indeed provide lattices with the required stability properties provided the relevent parameters are chosen within the appropriate range as evaluated in an appendix.) In more recent writing [11] these authors have conceded that our examples [6,7,8] do show how "one can build (purely by hand) special lattices that would be locally stable against small perturbations". They nevertheless maintain their no frustration conjecture to the effect that "no such configurations are expected to ever emerge from any realistic cosmological phase transition".…”