Observational constraints on the free parameters of an interacting Bose-Einstein gas as a dark-energy model

Dark energy is modelled by a Bose-Einstein gas of particles with an attractive interaction. It is coupled to cold dark matter, within a flat universe, for the late-expansion description, producing variations in particle-number densities. The model's parameters, and physical association, are: $\Omega_{G0}$, $\Omega_{m0}$, the dark-energy rest-mass energy density and the dark-matter term scaling as a mass term, respectively; $\Omega_{i0}$, the self-interaction intensity; $x$, the energy exchange rate. Energy conservation relates such parameters. The Hubble equation omits $\Omega_{G0}$, but also contains $h$, the present-day expansion rate of the flat Friedman--Lem\^aitre--Robertson--Walker metric, and $\Omega_{b0}$, the baryon energy density, used as a prior. This results in the four effective chosen parameters $\Omega_{b0}$, $h$, $\Omega_{m0}$, $\Omega_{i0}$, fit with the Hubble expansion rate $H(z)$, and data from its value today, near distance, and supernovas. We derive wide $1\sigma$ and $2\sigma$ likelihood regions compatible with definite positive total CDM and IBEG mass terms. Additionally, the best-fit value of parameter $x$ relieves the coincidence problem, and a second potential coincidence problem related to the choice of $\Omega_{G0}$.