**3.2.3. Cluster Abundance Versus the COBE Normalisation**

There are a number of ways to infer
_{8} from galaxy clustering
and peculiar velocity fields. The problem with the information from
galaxy clustering is that it involves an unknown biasing factor,
which hinders us from determining an accurate
_{8}.
The velocity data are susceptible to noise from the distance
indicators. Therefore, the cluster abundance discussed above
seems to give us a unique method to derive an accurate estimate of
_{8} for a low *z*
universe. Another place
we can extract an accurate
_{8} is the fluctuation power
imprinted on cosmic microwave background radiation (CBR)
anisotropies. Currently only the COBE observation
(Bennett et al. 1996)
gives sufficiently accurate
_{8} =
_{8}(*H*_{0},
,
,
_{B}, ...). Assuming the
model transformation function, the matching
of COBE _{8} with that
from the cluster abundance gives a significant constraint
on cosmological parameters =
(*H*_{0},
)
(Efstathiou et
al. 1992;
Eke et al. 1996).
Figure 4 shows allowed regions for two
cases, open and flat universes, assuming a flat perturbation spectrum
*n* = 1
and ignoring possible tensor perturbations.

The transfer function is modified if *n*
1. The
possible presence of the tensor perturbations in CBR anisotropies causes
another uncertainty.
The COBE data alone say *n* being between 0.9 and 1.5
(Bennett et
al. 1996),
but the allowed range is narrowed to *n* = 0.9-1.2 if supplemented by
smaller angular-scale CBR anisotropy data
(Hancock et al. 1998;
Lineweaver 1998;
Efstathiou et
al. 1999;
Tegmark 1999).
The presence of the tensor mode would make the range of *n* more
uncertain as well as it reduces the value of
_{8}. The limit of
*n* when the tensor mode is maximally allowed
is about < 1.3 ^{(4)}.
Notwithstanding these uncertainties,
> 0.5 is difficult to
reconcile with the matching condition.
On the other hand, a too small
( 0.15) is not consistent
with the cluster abundance.