© CAMBRIDGE UNIVERSITY PRESS 1983, 1993

1.10 Relativistic Cosmology

If Hubble's observation launched modern observational cosmology, it was Einstein's general theory of relativity that laid the foundations of modern theoretical cosmology. We will discuss in Chapter 3 the details of how the theoretical developments in cosmology actually began more than a decade before Hubble's exciting observations. We conclude the present chapter by considering the general question of why relativity is taken to be so important for cosmology.

Table 1.4. Spatial dimensions and masses of astronomical systems

Object	Linear size	Mass
Sun	7 x 1010 cm (radius)	2 x 1033 g M
Galaxy	15 kpc	1011 M
Cluster	5 Mpc	1013-1014 M
Supercluster	50 Mpc	1015 M
Universe	3000 Mpc	1021 M

Table 1.4 shows the orders of magnitude involved in the large-scale structure of the universe. The last entry refers to the characteristic distance scale c / H₀ that emerges from Hubble's constant and the mass contained in the ``observable'' volume of radius c / H₀ if the density were that seen for visible matter in our neighbourhood. Similarly, the time scale characteristic of the universe is H₀^-1 10¹⁰ years.

What interaction in physics is likely to be influential over such long distances and such large masses? Of the four known interactions, only gravity and electromagnetism are of long range. Although the electromagnetic interaction is much stronger than gravity on the scale of atoms, it is ineffective in determining the large-scale structure of the universe, since all indications are that an electric charge balance is preserved in galaxies, clusters, and intergalactic space. Nor is there any evidence for large-scale electric currents that could interact with the magnetic fields in the universe to produce large forces. By contrast, the enormous masses of astronomical objects generate huge gravitational fields. Gravity is therefore the most relevant force in cosmology.

Given that we need a theory of gravity for cosmology, what is wrong with the Newtonian framework? It has worked well in the theory of stellar structure. It is even used in stellar dynamics in the Galaxy. Why not use it in cosmology? Let us try to understand the answer with the help of the entries in Table 1.4.

Newtonian gravity is a theory of instantaneous action at a distance. As such, it is inconsistent with the special theory of relativity, in particular with the limit (c) placed by that theory on the speed with which any interaction can propagate across space. In those parts of astronomy where the distances across which gravity is suppose to act are relatively small, the use of Newtonian gravity is permissible. As seen in Table 1.4, however, the distances in cosmology are so large that action at a distance with infinite speed is unrealistic. This is not so with stellar dimensions or even for galaxies.

Special relativity itself is suspect in the presence of gravity. The concepts of the inertial frame and the inertial observer (on whom no force acts), which are so basic to special relativity, are unrealizable in the presence of gravity. Gravity seems to be an ever-present force that cannot be switched off altogether. Since all matter attracts gravitationally, an inertial observer cannot exist at all! Nevertheless, it was shown in 1934 by E.A. Milne and W.H. McCrea that with suitable compromise Newtonian gravity and special relativity can describe cosmology in an adequate manner. Although Newtonian cosmology is simple to understand, it is based on insecure foundations. It is preferable instead to resort to a framework that is free from conceptual difficulties and compromises.

As we shall see in Chapter 2, general relativity provides a framework that is free from the difficulties of Newtonian gravity with respect to special relativity and of special relativity with respect to gravity. It is for these conceptual reasons, apart from the experimental successes of general relativity in the various solar system experiments (see section 2.10), that cosmologists feel at home with the use of this theory.

It is therefore appropriate that we begin our discussion of cosmology by outlining the general theory of relativity.