184 Cosmic Microwave Background
The gravitational redshift and the time dilation both contribute to훿푇∕푇 0 by
amounts which are linearly dependent on the density fluctuations훿휌∕휌, so the net
effect is given by
훿푇
푇≃^1
3
(
퐿dec
푐푡dec) 2
훿휌
휌
, (8.23)
where퐿decis the size of the structure at decoupling time푡dec[corresponding to푧decin
Equation (5.76)]. [Note that Equation (8.23) is strictly true only for a critical universe
with zero cosmological constant.]
The space-time today may also be influenced by primordial fluctuations in the met-
ric tensor. These would have propagated as gravitational waves, causing anisotropies
in the microwave background and affecting the large-scale structures in the Universe.
High-resolution measurements of the large-angle microwave anisotropy are expected
to be able to resolve the tensor component from the scalar component and thereby
shed light on our inflationary past.
Further sources of anisotropies may be due to variations in the values of cosmo-
logical parameters, such as the cosmological constant, the form of the quintessence
potential, and local variations in the time of occurrence of the LSS.
Discovery. For many years microwave experiments tried to detect temperature vari-
ations on angular scales ranging from a few arc minutes to tens of degrees. Ever
increasing sensitivities had brought down the limits on훿푇∕푇 to near 10−^5 without
finding any evidence for anisotropy until 1992. At that time, the first COBE observa-
tions of large-scale CMB anisotropies bore witness of the spatial distribution of inho-
mogeneities in the Universe on comoving scales ranging from a few hundred Mpc
up to the present horizon size, without the complications of cosmologically recent
evolution. This is inaccessible to any other astronomical observations.
On board the COBE satellite there were several instruments, of which one, the
DMR, received at three frequencies and had two antennas with 7∘opening angles
directed 60∘apart. This instrument compared the signals from the two antennas, and
it was sensitive to anisotropies on large angular scales, corresponding to multipoles
퓁<30. Later radio telescopes were sensitive to higher multipoles, so one now has a
detailed knowledge of the multipole spectrum up to퓁=2800.
The most precise recent results are shown in Figure 8.3. At low 퓁,the
temperature–power spectrum is smooth, caused by the Sachs–Wolfe effect. Near
퓁=200 it rises towards the first and dominant peak of a series ofSakharov oscilla-
tions, also confusingly called theDoppler peak. They are basically caused by density
perturbations which oscillate as acoustic standing waves inside the LSS horizon. The
exact form of the power spectrum is very dependent on assumptions about the matter
content of the Universe; thus careful measurement of its shape yields precise infor-
mation about many dynamical parameters. For details of the results included in the
figure, see reference [6].
The definitive DMR results [4] cover four years of measurements of eight complete
mappings of the full sky followed by the above spherical harmonic analysis. The CMB