Despite the great progress in precise measurements of large-scale
structure, we cannot achieve a complete specification of the
cosmological model in this way alone. The vacuum energy is
not probed, since this affects mainly the growth rate of
structure - which is degenerate with bias evolution.
The matter content is only constrained if we assume that *n* = 1,
and even then we only measure
_{m} if a
value for *h* is supplied. A more complete picture is obtained if we
include data on clustering at much earlier times: the
anisotropy of the microwave background, which reaches us from
*z* 1100. In
addition to breaking degeneracies,
studies of this sort also test the basic gravitational
instability theory - which will be seen to work very well indeed
over this redshift range.
This section briefly reviews the physics of CMB
anisotropies, and presents recent data. For more details, see e.g.
Hu & Dodelson (2002),
or Dodelson (2003).

Fluctuations in the 2D temperature perturbation field are treated similarly to density fluctuations, except that the field is expanded in spherical harmonics, so modes of different scales are labelled by multipole number, . Once again, we can define a `power per octave' measure for the temperature fluctuations:

(136) |

where the *C*_{}
are another common way of representing the power. Note that
^{2}() is a power per
ln; the modern trend is
often to plot CMB fluctuations
with a linear scale for -
in which case one should really use
^{2}() /
.

We now list the mechanisms that cause primary anisotropies in the CMB (as opposed to secondary anisotropies, which are generated by scattering along the line of sight). There are three basic primary effects, illustrated in figure 16, which are important on respectively large, intermediate and small angular scales:

(1) Gravitational (Sachs-Wolfe) perturbations. Photons from high-density regions at last scattering have to climb out of potential wells, and are thus redshifted:

(137) |

(2) Intrinsic (adiabatic) perturbations. In high-density regions, the coupling of matter and radiation can compress the radiation also, giving a higher temperature:

(138) |

(3) Velocity (Doppler) perturbations. The plasma has a non-zero velocity at recombination, which leads to Doppler shifts in frequency and hence brightness temperature:

(139) |

To the above list should be added `tensor modes': anisotropies due to a background of primordial gravitational waves, potentially generated during an inflationary era (see below).

There are in addition effects generated along the line of sight. One important effect is the integrated Sachs-Wolfe effect, which arises when the potential perturbations evolve:

(140) |

This happens both at early times (because radiation is still important) and late times (because of ). Other effects are to do with the development of nonlinear structure, and are mainly on small scales (principally the Sunyaev-Zeldovich effect from IGM Comptonization). The exception is the effect of reionization; to a good approximation, this merely damps the fluctuations on all scales:

(141) |

where the optical depth must exceed
0.04, based on the
highest-redshift quasars and the BBN baryon density. As we will see
later, CMB polarization data have detected a signature consistent
with = 0.17± 0.04,
implying reionization at
*z* 20.