Poly-Essential and General Hyperelastic World (Brane) Models

Abstract

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model-the k-essential analogue of an ordinary polytropic fluid-is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio w is positive.

Stability of winding cosmic wall lattices with X type junctions

“…The winding stabilization mechanism for the superposed lasagne-type configurations envisaged here would work just as well if, instead of three (the minimum compatible with an isotropic total stress tensor) a higher number of independent scalar fields were invoked. In that case one would obtain more than triply superposed lasagne-type configurations which would be just as stable, but in which there would be too many degrees of freedom for the system to behave as a simple elastic (or even hyperelastic [26]) solid unless coupled with something else that ensured the required cohesion. The lack of a plausible cohesion mechanism was one of the weak points in the kinds of solid lattice scenarios that were originally considered.…”

Classical dynamics of strings and branes, with application to vortons

“…The hyperelastic category [29] (generalising the case of an ordinary elastic solid which includes the special case of an ordinary barotropic perfect fluid) consists of brane models in which -with respect to a suitably comoving internal reference system σ i -there are no independent surface fields at all -meaning that the ϕ α and the p α i are absent -and in which the only relevant background field is the metric g µν that is specified as a function of the external coordinates x µ . In any such case, the generic variation of the Lagrangian is determined just by the surface stress momentum energy density tensor T µν according to the standard prescription…”

Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defects

“…The work in the preceeding sections implies that the minimally extended Witten model with the same interaction potential V will give rise to an ensuing conducting string model that will be governed by the same equation of state, even though it will not be of the ordinary elastic type with q = p, but of the hyperelastic type [17] with q = p + 1, that is to say with a target space having a dimension that is equal to the space-time dimension of the supporting wordldsheet, namely p + 1 = 2 in the string case under consideration. It can be seen from the characteristic equation ( 27) that, according to (81), the speed c L of longitudinal sound type perturbations relative to the preferred reference system will be given in this hyperelastic case by…”

“…This is something that will be possible only if the target-space dimension q does not exceed the dimension d = p + 1 of the supporting base space, which if it is an embedded p-brane worldsheet can itself not exceed the dimension n of the background spacetime: q ≤ p + 1 ≤ n. The dimensionally maximal case q = p + 1 includes various models of the recently investigated kind [17] referred to a hyperelastic, while perfect solids [16] and so, in particular, ordinary fluid models of the barotropic type, are included in the case q = p.…”