Lorentzian manifolds with a special type of semi-symmetric non-metric connection and modified gravity

This paper investigates a spacetime equipped with a special type of semi-symmetric non-metric connection. If the associated vector field for this spacetime has some properties, then the nature of this spacetime has been investigated. On the other hand, we prove that this spacetime represents a perfect fluid spacetime as well as GRW spacetime. Moreover, we show that this spacetime reduces to stiff matter, dark matter era or Minkowski spacetime under some special conditions. In the third part of this paper, we consider [Formula: see text]-gravity as a modified gravity theory on this spacetime. Some remarkable theorems for such a spacetime are proved.