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(H0,
,
,
B, ...). Assuming the
model transformation function, the matching
of COBE 8 with that
from the cluster abundance gives a significant constraint
on cosmological parameters =
(H0,
)
(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.
|
Figure 4. Parameter regions allowed by
matching the rms fluctuations
from COBE with those from the cluster abundance. A flat spectrum
(n = 1) is assumed and the tensor perturbations are neglected.
The lower band is for a flat universe, and the upper one for a universe
with |
4 In Tegmark's analysis n < 1.5 is
quoted as an upper bound, but this is obtained by making
B (and
H0) a free parameter.
If one would fix the baryon abundance,
the allowed range is narrower, n
3.
Back.
= 0.