Cosmology is the study of the dynamics of the entire universe. The mathematical formulation of cosmology is relatively simpler due to two reasons. The first reason is that gravity dominates on large scales of space–time, so the local complexity arising from electromagnetic and nuclear forces, can be ignored. The second reason for simplicity is that the universe, on a large scale and to a good approximation, is homogeneous and isotropic. The incorporation of the characteristics of homogeneity and isotropy into the spatial part of the metric, enables us to consider spaces of constant curvature.
Consider an n-dimensional space Rn and let k designate its curvature. According to Schurs theorem from differential geometry, ...