  The recently introduced relativistic Lagrangian darkon fluid model (EPJ C
(2015) 75:9) is generalized to a self-gravitating, irrotational, pressure-less
and stress free geodesic fluid, whose energy-momentum tensor is dust-like with
nontrivial energy flow, defining the general framework for our cosmological
model. In the present paper we consider only the averaged dynamics of the
Universe at very large scales, allowing us to work with conformal flat
geometry. The corresponding covariant propagation and constraint equations are
treated in a shear-free nonrelativistic limit. The dynamics is described with a
Lagrangian in minisuperspace. Analytic solutions for the energy density, the
Hubble function and the 1st order relativistic correction to the spatial
curvature are obtained by means of two conditional dynamical symmetries. This
leads to a cosmological model where the accelerated expansion of the Universe
is driven by a time-dependent spatial curvature without the need for
introducing any kind of dark energy. A differential equation for the area
distance is derived in addition.
