The
expansion of the Universe
is described by the cosmic-scale factor
*R*(*t*). The expansion rate slows due to the attractive
action of gravity, denotes its present value.
If the average density is greater than the critical density
(density parameter ) the Universe
will eventually recollapse; otherwise ( ), the expansion
continues forever. A critical universe ( ) is spatially
flat; a high-density universe ( ) curves back on itself like
the surface of a ball; a low-density universe ( ) is
negatively curved like a saddle.

As the Universe expands, photons have their wavelengths stretched
(``redshifted'') proportional to *R*(*t*).
The measured redshift *z* of a photon of known wavelength
at emission (e.g., a spectral line) reveals the size of the Universe
when it was emitted, , as
well as the age,
(assuming a matter-dominated,
flat Universe with Hubble constant ).
The most distant galaxy observed has a redshift of 4.94, which means the
Universe was a factor of 5.94 smaller and about 0.9Gyr old when the light
we see now was emitted.

As the Universe expands, it cools adiabatically with temperature falling
as 1/*R*(*t*). At a temperature of around 3000K (energy equivalent
eV) the thermodynamic transition from ionized matter
to neutral matter occurred (called recombination); this drastically
and suddenly reduced the opacity
from Thomson scattering, so that ``last scattering'' of the CMB
photons occurred then. At this epoch CMB photons had
wavelengths corresponding to visible light and the
Universe was around 300,000 years old.

When the Universe was about a factor of 6000 times smaller than present ( eV and age of about ten-thousand years), the energy density in the thermal radiation (CMB photons) was comparable to that of matter (matter - radiation equality). At earlier times, radiation dominated the energy density, and density perturbations did not grow. During the time between matter - radiation equality and recombination only perturbations in the nonbaryonic dark matter grow because the baryons are supported against collapse by radiation pressure. (Once the Universe recombines baryons are released from the photons and fall into the dark-matter potential wells.) The extra growth of density perturbations for a universe with nonbaryonic dark matter means that a lower level of initial irregularity is needed to produce the structure seen today. This explains why a smaller level of CMB anisotropy is expected if there is nonbaryonic dark matter.

Sun Nov 2 13:44:30 CST 1997