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

**3.6. Parameters**

Now that the overall normalization of the CDM input power spectrum
has been measured, we return to the classic issues of the global parameters
(*H*_{0},
_{0}). Can
one consistently fit observations with the model
requirements? In a flat universe without a cosmological constant, the age is
*t* = 2 / (3*H*_{0}), so a small Hubble constant is
needed in order to avoid an age
for the universe that is less than that of constituent parts such as
globular
dusters. In addition, the need for relatively more large-scale power pushes
CDM in the direction of a small value of *H*_{0}. As a
result of these constraints,
those constructing global CDM models have typically adopted
*H*_{0} = 50 as
the *largest* possible value consistent with their requirements,
and *H*_{0} = 30
would be greatly preferable with regard to large-scale structure questions.
The observational situation is, as ever, unresolved. At present, most of the
modem indicators seem to produce values of *H*_{0} which
cluster in the 70-90 km s^{-1}/Mpc range
(van den Bergh 1989,
Tonry 1991),
and *H*_{0} = 50 is
at least one sigma below current best estimates. Thus, at about the
1.5
level (or worse), one can say that the observed value of
*H*_{0} is inconsistent with the needs of standard CDM.

Most estimates of
are also below the CDM requirement of unity, but
the long observed tendency for dynamical mass estimates to grow with
time and to increase with the scale of measurement leaves the issue in
substantial doubt. Clusters of galaxies, which should efficiently collect
dark matter due to the depth of their potential wells, typically indicate
*(M/L)*
250-300. Then, utilizing the observed light density of the
universe, one finds
= *(M / L)* / 1400
0.2. A similar, independent result
is obtained from clusters by another route. The ratio of baryonic-to-total
mass in the clusters is in the range (for *h* = 1) 10% to 15% with
most of
that in X-ray emitting gas. But, from light element nucleosynthesis, the
baryonic density is
_{b} = 0.013
*h*^{-2}. Then, dividing by the ratio of
baryonic-to-total mass from clusters gives an
_{tot}
<< 1, a point made by
White (1992)
and others.

There is currently one group of studies that does indicate a relatively
large value of from
direct dynamical measurements.
Dekel et al (1993)
(see also
Dekel 1991 and
Yahil 1990)
have combined the *IRAS* 2Jy survey
with redshifts from 10^{3.4} galaxies and reasonable assumptions
about the
velocity field to measure the dynamical mass density on approximately the
50 *h*^{-1} Mpc scale. They find that
= 1.4 ×
10^{±0.3}*b*^{5/3}, where *b*, the bias
of *IRAS* galaxy fluctuations over the mass fluctuations on a scale
of 12 *h*^{-1}
Mpc, may be slightly in excess of unity. While the 95% confidence limits
quoted above seem most consonant with a flat model, the result is still of
course consistent with open models and, in any case, replication by other
workers in other volumes of space is necessary.

Thus, the evidence on the crucial question of the actual value of is mixed. Almost all methods indicate 0.2-0.3 as a best fit, but one careful study is consistent with closure, = 1.