  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.
