  Starting from an affinely connected space, we consider a model of gravity
whose fundamental field is the connection. We build up the action using as sole
premise the invariance under diffeomorphisms, and study the consequences of a
cosmological ansatz for the affine connection in the torsion-free sector.
Although the model is built without requiring a metric, we show that the
nondegenerated Ricci curvature of the affine connection can be interpreted as
an \emph{emergent} metric on the manifold. We show that there exists a
parametrization in which the \((r,\varphi)\)-restriction of the geodesics
coincides with that of the Friedman--Robertson--Walker model. Additionally, for
connections with nondegenerated Ricci we are able to distinguish between
space-, time- and null-like self-parallel curves, providing a way to
differentiate \emph{trajectories} of massive and massless particles.
