88 An introduction to the physics of cosmology
In a famous piece of serendipity, the redshifted radiation from the last-
scattering photosphere was detected as a 2.73 K microwave background by
Penzias and Wilson (1965). Since the initial detection of the microwave
background atλ= 7 .3 cm, measurements of the spectrum have been made over
an enormous range of wavelengths, from the depths of the Rayleigh–Jeans regime
at 74 cm to well into the Wien tail at 0.5 mm. The most accurate measurements
come fromCOBE—the NASA cosmic background explorer satellite. Early data
showed the spectrum to be very close to a pure Planck function (Matheret al
1990), and the final result verifies the lack of any distortion with breathtaking
precision. The COBE temperature measurement and 95% confidence range of
T= 2. 728 ± 0 .004 Kimproves significantly on the ground-based experiments. The lack of distortion
in the shape of the spectrum is astonishing, and limits the chemical potential
to|μ| < 9 × 10 −^5 (Fixsenet al1996). These results also allow the limit
y. 1. 5 × 10 −^5 to be set on the Compton-scattering distortion parameter.
These limits are so stringent that many competing cosmological models can be
eliminated.
2.8.2 Mechanisms for primary fluctuations
At the last-scattering redshift (z1000), gravitational instability theory says
that fractional density perturbationsδ & 10 −^3 must have existed in order for
galaxies and clusters to have formed by the present. A long-standing challenge
in cosmology has been to detect the corresponding fluctuations in brightness
temperature of the CMB radiation, and it took over 25 years of ever more stringent
upper limits before the first detections were obtained, in 1992. The study of CMB
fluctuations has subsequently blossomed into a critical tool for pinning down
cosmological models.
This can be a difficult subject; the treatment given here is intended to be the
simplest possible. For technical details see, e.g., Bond (1997), Efstathiou (1990),
Hu and Sugiyama (1995), Seljak and Zaldarriaga (1996); for a more general
overview, see Whiteet al(1994) or Partridge (1995). The exact calculation of
CMB anisotropies is complicated because of the increasing photon mean free
path at recombination: a fluid treatment is no longer fully adequate. For full
accuracy, the Boltzmann equation must be solved to follow the evolution of the
photon distribution function. A convenient means for achieving this is provided
by the public domainCMBFASTcode (Seljak and Zaldarriaga 1996). Fortunately,
these exact results can usually be understood via a more intuitive treatment, which
is quantitatively correct on large and intermediate scales. This is effectively what
would be called local thermodynamic equilibrium in stellar structure: imagine
that the photons we see each originated in a region of space in which the radiation
field was a Planck function of a given characteristic temperature. The observed