Gravity and Dark Matter in the Framework of Metric-Affine Geometry

In this paper, we generalize space-time manifold by considering metric-affine structure on space-time manifold. Metric-affine geometry is defined in terms of two independent objects: the Riemannian metric and the general affine connection. With the help of the metric tensor for contraction of Riemannain curvature of the affine connection, we formed a natural action density for gravity and matter. Using calculus of variations we derive two equations. The first equation retrieves Einstein field equation. The other equation describes matter in space-time. In this framework, the affine connection is related to the concept that is well-known as dark matter, so dark matter can be interpreted as a factor which leads curving and twirling of space-time manifold.