The issue

The issue we plan to address in this book, that of the average density of matter in the universe, has been a central question in cosmology since the development of the first mathematical cosmological models. As cosmology has developed into a quantitative science, the importance of this issue has not dimininished and it is still one of the central questions in modern cosmology.

Why is this so? As our discussion unfolds, the reason for this importance should become clear, but we can outline three essential reasons right at the beginning. First, the density of matter in the universe determines the geometry of space, through Einstein's equations of general relativity. More specifically, it determines the curvature of the spatial sections: flat, elliptic or hyperbolic. The geometrical properties of space sections are a fundamental aspect of the structure of the universe, but also have profound implications for the space-time curvature and hence for the interpretation of observations of distant astronomical objects. Second, the amount of matter in the universe determines the rate at which the expansion of the universe is decelerated by the gravitational attraction of its contents, and thus its future state: whether it will expand forever or collapse into a future hot big crunch. Both the present rate of expansion and the effect of deceleration also need to be taken into account when estimating the age of the universe.