9 Cosmic microwave background anisotropies
After recombination, the primordial radiation freely streams through the universe
without any further scattering. An observer today detects the photons that last
interacted with matter at redshiftz≈1000, far beyond the stars and galaxies. The
pattern of the angular temperature fluctuations gives us a direct snapshot of the
distribution of radiation and energy at the moment of recombination, which is
representative of what the universe looked like when it was a thousand times smaller
and a hundred thousand times younger than today.
The first striking feature is that the variations in intensity across the sky are tiny,
less than 0.01% on average. We can conclude from this that the universe was ex-
tremely homogeneous at that time, in contrast to the lumpy, highly inhomogeneous
distribution of matter seen today. The second striking feature is that the average
amplitude of the inhomogeneities is just what is required in a universe composed
of cold dark matter and ordinary matter to explain the formation of galaxies and
large-scale structure. Moreover, the temperature autocorrelation function indicates
that the inhomogeneities have statistical properties in perfect accordance with what
is predicted by inflationary models of the universe.
In a map showing the microwave background temperature across the sky, the
features subtending a given angle are associated with physics on a spatial scale
that can be computed from the angle and the angular diameter distance to the last
scattering surface. The latter depends on the cosmological model. The angular scale
θ∼ 1 ◦corresponds to the Hubble radius at recombination, which is the dividing
line between the large-scale inhomogeneities that have not changed much since
inflation and the small-scale perturbations that have entered the horizon before re-
combination and been substantially modified by gravitational instability. Hence,
observations of temperature fluctuations on large angular scales give us direct in-
formation about the primordial spectrum of perturbations, and observations of the
small-scale fluctuations enable us to determine the values of the cosmological
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