  Whereas the nature of dark components in the Universe remains unknown,
alternative models of gravity have been developed to offer a geometric
explanation to the origin of such components. In this work we use the Minimal
Geometric Deformation approach to study extensions of the theory of General
Relativity in a cosmological context. This is possible since such approach
allows the decoupling of gravitational sources, and the Einstein field
equations can be analytically solved with the presence of a new gravitational
sector once a known GR solution is considered. In particular, we implement such
approach in Friedmann-Robertson-Walker and Kantowski-Sachs universes. We
demonstrate that the gravitational decoupling leads to modifications of well
known cosmological solutions. For instance, we show that an effective spatial
curvature in the Friedmann-Robertson-Walker metric, as well as several kind of
matter components in the Kantowski-Sachs case, are obtained. Thus, we found
that it is possible to obtain spatial curvature and new matter terms from
geometry, which in cosmology they could be useful in addressing problems such
as the spatial flatness of the Universe, dark matter and dark energy.
