100 An introduction to the physics of cosmology
The physical degree of freedom here can be thought of as the Hubble
constant. This is involved via the relation
h^2 =ωm+ωv+ωk,so specifyinghin addition to the physical matter density fixesωv+ωkand
removes the degeneracy.
2.8.7 Small-scale data and outlook
The study of large-scale CMB anisotropies had a huge impact on cosmology in
the 1990s, and the field seems likely to be of increasing importance over the next
decade. This school was held at a particularly exciting time, as major new data
on the CMB power spectrum arrived during the lectures (de Bernardiset al2000,
Hananyet al2000). Although these developments are very recent, the situation
already seems a good deal clearer than previously, and it is interesting to try to
guess where the field is heading.
One immediate conclusion is that it increasingly seems that the relevant
models are ones in which the primordial fluctuations were close to being adiabatic
and Gaussian. Isocurvature models suffer from the high amplitude of the large-
scale perturbations, and do not become any more attractive when modelled in
detail (Huet al1995). Topological defects were for a long time hard to assess,
since accurate predictions of their CMB properties were difficult to make. Recent
progress does, however, indicate that these theories may have difficulty matching
the main details of CMB anisotropies, even as they are presently known (Penet
al1997).
We shall therefore concentrate on interpreting the data in terms of the
simplest gravitational-instability models. Many of the features of these models
are generic, although they are often spoken of as ‘the inflationary predictions’.
This statement needs to be examined carefully, since one of the possible prizes
from a study of the CMB may be a test of inflation. CMB anisotropies in
theories where structure forms via gravitational collapse were calculated in
largely the modern way well before inflation was ever considered, by Peebles
and Yu (1970). The difficulty in these calculations is the issue of super-
horizon fluctuations. In a conventional hot big bang, these must be generated by
some acausal process—indeed, an acausal origin is required even for large-scale
homogeneity. Inflation is so far the only theory that generates such superhorizon
modes at all naturally. Nevertheless, it is not acceptable to claim that detection
of super-horizon modes amounts to a proof of inflation. Rather, we need some
more characteristic signature of the specific process used by inflation: amplified
quantum fluctuations.
We should thus review the predictions that simple models of inflation make
for CMB anisotropies (see, e.g., chapter 11 of Peacock 1999 or Liddle and Lyth
2000 for more details). Inflation is driven by a scalar fieldφ, with a potential