  In this work we provide the motivation for considering non-Riemannian models
in cosmology. Non-Riemannian extensions of general relativity theory have been
studied for a long time. In such theories the spacetime continuum is no longer
described by the metric alone but endowed with additional geometric quantities.
These new quantities can be coupled to the intrinsic properties of matter in a
very natural way and therefore provide a richer gravitational theory, which
might be necessary in view of the recent cosmological evidence for dark matter
and dark energy. In this work we mainly focus on the concepts in metric-affine
gravity and point out their possible significance in the process of
cosmological model building.
