Poly-essential and general Hyperelastic World (brane) models

TL;DR

This paper develops a unified framework for hyperelastic models of the universe, including fluids and solids, using energy-momentum conservation and symplectic structures to analyze perturbations and stability.

Contribution

It introduces a generalized hyperelastic framework for cosmological models, encompassing fluids and elastic solids, with new methods for analyzing perturbations and stability.

Findings

Poly-essential models are well-behaved only if pressure to density ratio is positive.

A generalized Hadamard operator constructs a symplectic structure for perturbation evolution.

Unified treatment of various non-linear classical field models of the universe.

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.