This thesis can be divided in two parts. First part is a review on modern cosmology. Cosmology is known as one of the main outcomes of general relativity and most books on general relativity end with a more or less brief discussion about cosmology. Cosmology and related subjects are vastly studied in the recent two decades. The present thesis pays special attention to the mathematical foundations of cosmology and provides basic information about main topics in modern cosmology, like the cosmic microwave background, dark energy and the different cosmological eras. According to scientists, cosmology exploits almost all parts of physics, from elementary particles up to gravity and general relativity, optics, statistical mechanics and plasma. An explanation of its diverse phenomena and an appropriate research on cosmology demands a minimum knowledge of all of these fields. In this project the main concepts of cosmology is presented and an accurate inquiry is preferred over an extensive but less accurate review. The second part of this thesis casts to the non-commutativity idea and its probable relation with gravity. In this part after studying the prerequisites regarding the non-commutative space and the way in which we can perform calculations in this space, the corrections to the Kerr metric has been calculated. In previous articles, other well known metric solutions of general relativity like the Schwarzschild and Robertson-Walker metric were extended to the non-commutative space and some expected results were discussed. In this thesis, the Kerr metric as the metric describing the geometry of most of the known black holes in the universe has been extended to the non-commutative space and some probable results of this generalization on the event horizon of the black holes and the red shift of the light of luminous subjects falling in the black hole are being discussed. Keywords: Standard model of cosmology, Cosmological eras, Kerr metric, non-commutative space
