Introduction

This chapter applies the general theory of relativity to the study of cosmology and the evolution of the universe. Our emphasis will be mostly on the geometrical aspects of the universe rather than on physical cosmology. However, in order to provide a complete picture and to appreciate the interplay between theory and observation, it is necessary to discuss certain aspects of the evolutionary history of the universe. We shall do this in Section 10.6 even though it falls somewhat outside the main theme of development.

The Friedmann spacetime

Observations show that, at sufficiently large scales, the universe is homogeneous and isotropic; that is, the geometrical properties of the three-dimensional space: (i) are the same at all spatial locations and (ii) do not single out any special direction in space.

The geometrical properties of the space are determined by the distribution of matter through Einstein's equations. It follows, therefore, that the matter distribution should also be homogeneous and isotropic. This is certainly not true at small scales in the observed universe, where a significant degree of inhomogeneity exits in the form of galaxies, clusters, etc. We assume that these inhomogeneities can be ignored and the matter distribution may be described by a smoothed out average density in studying the large scale dynamics of the universe.