ABSTRACT

The uniform model universes based on the Robertson–Walker separation formula (6.1.3) are characterised by their scale factors R(t) and ‘curvature index’ k. According to (6.1.1), these quantities determine the curvature K(t) of three-dimensional position space at cosmic time t. What determines R(t) and k? The answer is: the self-gravitation of all the matter in the universe, since this must control the nature of the expansion. In a rigorous treatment, the curvature tensor of spacetime would be given, by Einstein’s field equations, in terms of the tensor describing the distribution of cosmic matter. However, such generality involves mathematics too advanced for the present work, and we find the connection between curvature and matter by using arguments similar to those of section 4.4.