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.

FURTHER READING:

Harrison, E.R., `Fluctuations at the threshold of classical
cosmology', *Physical Review* D, 1970, **1**, 2726.
Zel'dovich, Ya.B., `A hypothesis unifying the structure and entropy of
the Universe', *Monthly Notices of the Royal Astronomical Society*,
1972, **160**, 1P.