  We find possible cosmological models of the Polynomial Affine Gravity
described by connections that are either compatible or not with a metric. When
possible, we compare them with those of General Relativity. We show that the
set of cosmological vacuum solutions in General Relativity are a subset of the
solutions of Polynomial Affine Gravity. In our model the cosmological constant
appears as an integration constant, and additionally, we show that some forms
of matter can be emulated by the affine structure---even in the metric
compatible case. In the case of connections not compatible with a metric, we
obtain formal families of solutions, which should be constrained by physical
arguments. We show that for a certain parametrisation of the connection, the
affine Ricci flat condition yield the cosmological field equations of General
Relativity coupled with a perfect fluid, pointing toward a geometrical
emulation of---what is interpreted in General Relativity as---matter effects.
