  The existence of current-time universe's acceleration is usually modeled by
means of two main strategies. The first makes use of a dark energy barotropic
fluid entering \emph{by hand} the energy-momentum tensor of Einstein's theory.
The second lies on extending the Hilbert-Einstein action giving rise to the
class of extended theories of gravity. In this work, we propose a third
approach, derived as an intrinsic geometrical effect of space-time, which
provides repulsive regions under certain circumstances. We demonstrate that the
effects of repulsive gravity naturally emerge in the field of a homogeneous and
isotropic universe. To this end, we use an invariant definition of repulsive
gravity based upon the behavior of the curvature eigenvalues. Moreover, we show
that repulsive gravity counterbalances the standard gravitational attraction
influencing both late and early times of the universe evolution. This
phenomenon leads to the present speed up and to the fast expansion due to the
inflationary epoch. In so doing, we are able to unify both dark energy and
inflation in a single scheme, showing that the universe changes its dynamics
when ${\ddot H\over H}=-2\dot H$, at the repulsion onset time where this
condition is satisfied. Further, we argue that the spatial scalar curvature can
be taken as vanishing because it does not affect at all the emergence of
repulsive gravity. We check the goodness of our approach through two
cosmological fits involving the most recent union 2.1 supernova compilation.
