Extra-dimensional metamaterials: simple models of inflation and metric signature transitions

TL;DR

This paper models higher-dimensional lattice structures as metamaterials, demonstrating how they can emulate metric signature transitions and cosmological inflation through effective medium theory in a 4+1 dimensional electrodynamics framework.

Contribution

It introduces a novel approach to describe topological defect lattices as extra-dimensional metamaterials, linking their properties to metric signature transitions and inflation-like phenomena.

Findings

Abrikosov lattice states can be modeled as uniaxial hyperbolic metamaterials.

Metric signature of the effective spacetime depends on lattice periodicity.

The model can emulate cosmological inflation through medium effects.

Abstract

Lattices of topological defects, such as Abrikosov lattices and domain wall lattices often arise as metastable ground states in higher-dimensional field theoretical models. We demonstrate that such lattice states may be described as extra-dimensional metamaterials via higher-dimensional effective medium theory. A 4+1 dimensional extension of Maxwell electrodynamics with a compactified time-like dimension has been considered as an example. It is demonstrated that from the point of view of macroscopic electrodynamics an Abrikosov lattice state in such a 4+1 dimensional spacetime may be described as a uniaxial hyperbolic metamaterial. Extraordinary photons perceive this medium as a 3+1 dimensional Minkowski spacetime in which one of the original spatial dimensions (the optical axis of the metamaterial) plays the role of a new time-like coordinate. Since metric signature of this effective space-time depends on the Abrikosov lattice periodicity, the described model may be useful in studying metric signature transitions. A particular kind of metric signature transition understood as a macroscopic medium effect may emulate cosmological inflation.