Assessing the foundation and applicability of some dark energy fluid models in the Dirac–Born–Infeld framework

In this paper, we will deepen the understanding of some fluid models proposed by other authors for description dark energy. Specifically, show that so-called (Modified) Berthelot is hydrodynamic realization free Dirac–Born–Infeld (DBI) theory and Dieterici admits a nonrelativistic [Formula: see text]-essence formulation; former model evolution scalar field be written in terms cosmographic parameters. The latter also tested using Machine Learning algorithms with respect to cosmic chronometers data, results about dynamics at background level compared those arising when fluids (Generalized Chaplygin Gas Anton-Schmidt) are considered. Due opacity effects, cosmology universes filled these inequivalent fluids, as they arise physically different theories, may not enough discriminating among them. Thus, perturbation analysis long-wavelength limit carried out revealing rich variety possible behaviors. It shown DBI cannot account flat galactic rotation curves, therefore derive an appropriate relationship between potential brane tension achieving goal; provides estimate matter adiabatic speed sound inside halo consistent literature. A certain Newtonian gravitational within galaxy Lagrangian regime enlightened.