Essay

PRIMORDIAL DENSITY FLUCTUATIONS

Adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology, Routledge Inc., New York. Reprinted with the author's permission. To order this book click here: http://www.routledge-ny.com/books.cfm?isbn=0415923549

The standard theory of how cosmological structure formation is thought to have occurred is based on the idea of gravitational instability (Jeans instability), according to which small initial irregularities in the distribution of matter become amplified by the attractive nature of gravity. This idea explains, at least qualitatively, how it is possible for the high degree of inhomogeneity we observe around us to have arisen from a much more regular initial state. But gravitational instability would not have worked unless there were small fluctuations in the density at early times, so a complete theory of structure formation must explain how these initial fluctuations got there and predict their vital characteristics.

Since the mid-1980s there have emerged two rival views of how these initial seed fluctuations might have arisen, and they gave rise to two distinct theories of how the large-scale structure of the Universe was put in place. One of these models involved the idea of topological defects created during a phase transition in the early Universe. Phase transitions can be thought of as acting like regions of trapped energy, and they do drastic things to the distribution of matter around them: cosmic strings and global textures, in particular, were thought to have affected the early Universe sufficiently to seed density fluctuations directly. The theory of these kinds of fluctuation is difficult, however, because the physics is essentially nonlinear from the start. Although many researchers worked on these defect theories in the 1980s and early 1990s, their efforts have produced few concrete predictions.

The alternative picture involves the inflationary Universe. Inflation relies on the existence of a quantum scalar field whose vacuum energy drives the Universe into an accelerated expansion, ironing out any wrinkles and simultaneously decreasing the curvature of spacetime virtually to zero (see flatness problem, horizon problem). But the scalar field also produces small fluctuations because of quantum fluctuations in it, essentially arising from Heisenberg's uncertainty principle (see quantum mechanics). The initial fluctuations arising from inflationary models are much simpler than in the case of topological defects: the quantum fluctuations are small. so that methods from perturbation theory can be used. They are also statistically simple: the density field resulting from quantum fluctuations is of the simplest form known in probability theory - the form which is known as a Gaussian random field. The properties of such a field are described completely by the power spectrum of the fluctuations. In inflationary models the appropriate power spectrum is of a form known as the scale-invariant spectrum, which was derived (for an entirely different purpose) in the 1970s independently by Edward Harrison and by Yakov Zel'dovich.

This scale-invariant spectrum is particularly important because we know from very simple arguments that the Universe has to possess fluctuations that are nearly scale-invariant. The term `scale-invariant' means that fluctuations in the metric (the equivalent in Newtonian language to fluctuations in the gravitational potential) have the same amplitude on all scales. We know that the fluctuations in the cosmic microwave background radiation have an amplitude of around 10^-5; since these are thought to be generated by the Sachs-Wolfe effect, this number is of the same magnitude as that of the metric fluctuations. The scale in question here is the scale of our horizon: several thousand megaparsecs. But we can also look at individual galaxy clusters, which are less than 10 Mpc across. The random motions in these clusters, of around a thousand kilometres per second, can be related using the virial theorem to the gravitational potential energy of the cluster; we find that the gravitational potential energy is about 10^-5 of the total rest mass. This is no coincidence if the initial fluctuations are scale-invariant, as these are two independent measurements of the metric fluctuations on two very different length scales.

The detection of temperature anisotropies in the cosmic microwave background radiation (the famous ripples) with properties which are consistent with an inflationary origin left most cosmologists in little doubt that the density fluctuations were indeed of this nature. Subsequent finer-scale observations and more detailed calculations of the predictions of defect theories have confirmed this preliminary view. Topological defects are now, to most cosmologists, of only abstract theoretical interest.