  The polynomial affine gravity is an alternative model of gravity whose
fundamental field is the affine connection, and it is invariant under the
complete group of diffeomorphisms. In 3+1 dimensions the field equations
generalise those of Einstein--Hilbert, the coupling constants are
dimensionless, the action has a finite numbers of term, and although the action
does not involve a (fundamental) metric, some metric tensor fields might
\emph{emerge} from the connection. Provided a cosmological ansatz, the
properties of diverse cosmological models are discussed.
