Cosmology

regions, including the very center, may be dominated by black holes or other relativistic objects.) Galaxies are observed to form clusters, which often have thousands of members in a volume of the order of a Mpc. Such a cluster could have M/R 10−4, but it would still not need GR to describe it adequately.

When we go to larger scales than the size of a typical galaxy cluster, however, we enter the domain of cosmology.

In the cosmological picture, galaxies and even clusters are very small-scale structures, mere atoms in the larger universe. Our telescopes are capable of seeing to distances greater than 10 Gpc. On this large scale, the universe is observed to be homogeneous, to have roughly the same density of galaxies, and roughly the same types of galaxies, everywhere. As we shall see later, the mean density of mass–energy is roughly ρ = 10−26 kg m−3. Taking this density, the mass M = 4πρR3/3 is equal to R for R 6 Gpc, which is well within the observable universe. So to understand the universe that our telescopes reveal to us, we need GR.

Indeed, GR has provided scientists with their first consistent framework for studying cosmology. We shall see that metrics exist that describe universes that embody the observed homogeneity: they have no boundaries, no edges, and are homogeneous everywhere. Newtonian gravity could not consistently make such models, because the solution of Newton’s fundamental equation 2 = 4π Gρ is ambiguous if there is no outer edge on which to set a boundary condition for the differential equation. So only with Einstein could cosmology become a branch of physics and astronomy.

We should ask the converse question: if we live in a universe whose overall structure is highly relativistic, how is it that we can study our local region of the universe without reference to cosmology? How can we, as in earlier chapters, apply general relativity to the study of neutron stars and black holes as if they were embedded in an empty asymptotically flat spacetime, when actually they exist in a highly relativistic cosmology? How can astronomers study individual stars, geologists individual planets, biologists individual cells – all without reference to GR? The answer, of course, is that in GR spacetime is locally flat: as long as your experiment is confined to the local region you don’t need to know about the large-scale geometry. This separation of local and global is not possible in Newtonian gravity, where even the local gravitational field within a large uniform-density system depends on the boundary conditions far away, on the shape of the distant “edge” of the universe (see Exer. 3, § 12.6). So GR not only allows us to study cosmology, it explains why we can study the rest of science without needing GR!

The cosmological arena

In recent years, with the increasing power of groundand space-based astronomical observatories, cosmology has become a precision science, one which physicists look to for answers to some of their most fundamental questions. The basic picture of the universe that observations reveal is remarkably simple, when averaged over distance scales much larger than, say, 10 Mpc. We see a homogeneous universe, expanding at the same rate everywhere. The universe we see is also isotropic: it looks the same, on average, in every