Annu. Rev. Astron. Astrophys. 1993. 31:
689-716
Copyright © 1993 by . All rights reserved |

After successively lower and lower limits were set to the upper bound
on the quadrupole component by many experiments [the best prior
limit was given by the *Relikt* satellite
(Klypin et al 1987)],
the *COBE* DMR team announced
(Smoot et al 1992)
a value of *Q*_{rms} = 13 ± *µ*k or
*T / T* = 5 ×
10^{-6}. At 10° (full width Gaussian window), the
*COBE* team found
*T*_{rms} =
30 ± 5*µ*k, fixing the amplitude at that scale (comoving
wavelength ~ 300
_{0}^{-0.4} *h*^{-1}
Mpc). Since this value is based on observations at
several frequencies (which permit one to check that the fluctuations have
the correct spectral signature) and on many independent areas far from
the ecliptic and the Galactic plane, this result should be reliable. The
*COBE* team also found that, over the angular scales investigated, the
power-law spectral index *n* was determined to be *n* = 1.1
± 0.6, providing
(weak) support for the HZP value, *n* = 1, but allowing
considerable room for revision. According to
Efstathiou et al (1992),
the *COBE* measurements imply an amplitude on the galactic scale of
_{8} = 1.08
± 0.25; other groups (e.g.
Wright et al 1992)
find a similar value.

Smaller scale measurements of CBR fluctuations are both less conclusive
and more difficult to interpret. For the standard recombination picture,
the horizon at last scattering is approximately 2°. This could
increase to
nearly 10° for maximal reionization, but in general for scales smaller
than those of the *COBE* instrument, post recombination effects must be
considered. The 6° ULISSE
(de Bernardis et al
1992)
balloon experiment
gives an upper limit about 1.4 times the CDM prediction (normalized to
*COBE*), and it is therefore consistent with the model.

At the 1.5° scale, the
Gaier et al (1992)
south pole experiment sets a 95% confidence level upper bound of
(*T / T*)
1.4 ×
10^{-5}. This is quite close to the CDM prediction of
(*T/T*) = 1.3
× 10^{-5} for the *COBE*
normalization. The Owens Valley "Ring" experiment set a limit on the 2.6'
scale of (*T / T*)
< 1.9 × 10^{-5}
(Myers et al 1993)
and now appears to have
detected fluctuations (at the 95% confidence level). After removal of
contamination due to foreground nonthermal extragalactic radio sources, the
authors estimate (*T /
T*) = 3.3 × 10^{-6} on the 1-5 arcminute scale. This is
considerably above the CDM prediction of 1.0 × 10^{-6} but
within the range of what might be expected due to secondary processes
(Ostriker & Vishniac
1986,
Vishniac 1987).

These secondary effects, caused by interactions between CBR photons
and moving or heated electrons, were described initially by
Zeldovich & Sunyaev
(1969).
Since they are intrinsically due to nonlinear processes,
and highly dependent on the distribution of shock-heated gas, a full
hydrodynamic treatment is required.
Scaramella et al (1993)
summarize earlier
work and present the latest results for a CDM model. They find that the
small-scale fluctuations have, as expected, a strong non-Gaussian tail with
high values of (*T /
T*) following a roughly log-normal distribution. The
mean level of (*T /
T*) is due to heated gas at relatively large redshift and is
unobservably small (*y*
10^{-5.5}). The fluctuating component is due
primarily to low redshift heated gas (observationally identified
primarily with
clusters of galaxies). The thermal component of the secondary fluctuations
is found to be (*T /
T*)_{rms}
0.8 ×
10^{-6}
( /
10°)^{-1/4} for the *COBE* normalization, and for
_{b} =
0.06. This makes a negligible correction on the
*COBE* scales but approaches significance at the 3' Ring experiment
scale.
The velocity component of the total secondary fluctuations is typically an
order of magnitude smaller than the thermal component.

In sum, the CDM model, after normalization to the *COBE* DMR 10°
measurement, is in accord with all other CBR measurements except insofar
as it may predict a slight excess at small angular scales, corresponding to
the few Mpc comoving length scales. As we shall see, this defect recurs as
other observational tests are made on that scale.