Magnetic Seed and Cosmology as Quantum Hall Effect

TL;DR

This paper explores a novel analogy between modified Friedmann equations in a bimetric cosmological model and the quantum Hall effect, revealing regimes that could explain dark energy and primordial magnetic fields.

Contribution

It introduces a mapping between cosmological evolution and quantum Hall physics, proposing a new perspective on dark energy and magnetic field origins.

Findings

Two regimes identified: cosmological constant dominated and magnetic seed dominated.

Exponential expansion linked to cosmological constants.

Quantum Hall effect analogy provides insights into primordial magnetic fields.

Abstract

In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect.