Quintessence interacting dark energy and a scalar dark fluid from 5D vacuum

Considering a five-dimensional (5D) spacetime empty of matter, we develop a procedure from which an interacting scalar field and its potential are induced on our 4D spacetime by the 5D geometry. We use the procedure to derive a new 4D interacting quintessence scenario, where the quintessence field, its potential and the interaction between the dark matter and dark energy components have a geometrical origin. The mass of the interacting quintessence field depends on the extra dimension, thus giving more freedom to avoid conflicts with nucleosynthesis. Then, inspired from some scalar dark matter models, we extend the geometrical formalism to derive a novel 4D late-time cosmological scenario, where the whole dark sector of the universe (scalar dark matter plus dark energy) admits a unified description by a single geometrical scalar field.