86 An introduction to the physics of cosmology
Figure 2.18. The power spectrum for a galaxy catalogue constructed from theCDM
model. A reasonable agreement with the APM data (full line) is achieved by simple
empirical adjustment of the occupation number of galaxies as a function of halo mass,
plus a scheme for placing the halos non-randomly within the halos. In contrast, the galaxy
power spectrum differs significantly in shape from that of the dark matter (linear and
nonlinear theory shown as in figure 2.16).
correlations automatically follow the slope of the halo density profile, which
keeps them steep. The results of this exercise are shown in figure 2.18.
The results of this simple model are encouragingly similar to the scale-
dependent bias found in the detailed calculations of Bensonet al(2000a), shown
in figure 2.15. There are thus grounds for optimism that we may be starting to
attain a physical understanding of the origin of galaxy bias.
2.8 Cosmic background fluctuations
2.8.1 The hot big bang and the microwave background
What was the state of matter in the early phases of the big bang? Since the present-
day expansion will cause the density to decline in the future, conditions in the past
must have corresponded to high density—and thus to high temperature. We can
deal with this quantitatively by looking at the thermodynamics of the fluids that
make up a uniform cosmological model.
The expansion is clearlyadiathermal, since the symmetry means that there
can be no net heat flow through any surface. If the expansion is also reversible,
then we can go one step further, because entropy change is defined in terms of