It is tempting to believe that
_{m} is unity. If it is not
unity, one has to fine tune the initial curvature to one part in
10^{30}. Moreover inflationary models generally predict that
is unity. However the
evidence in favor of low
_{m}, and specifically
_{m}
0.3 is
mounting. The most
direct probe arises from counting rich galaxy clusters, both locally
and as a function of redshift. The direct prediction of
_{m} = 1 is that there
should be a higher-than-observed local density of clusters,
and strong evolution in number with redshift that is not seen.
^{18}
However this conclusion has recently been disputed.
^{19}
^{,20}

An indirect argument comes from studies of Type Ia supernovae, which
provide strong evidence for acceleration. This is most simply
interpreted in terms of a positive cosmological
constant.
^{21}
^{,22} The
SN Ia data actually measure
_{} -
_{m}. Combined with
direct measures of
_{m} both from galaxy
peculiar velocities and from
clusters, one infers that _{}
0.7. Hence
flatness is likely, and certainly well within observational
uncertainties. Further evidence for the universe being spatially flat
comes from the measurement of the location of the first acoustic peak
in the cosmic microwave background anisotropy spectrum. The location
reflects the angular size subtended by the horizon at last scattering,
and has Fourier harmonic *l* = 220
^{-1/2}. Current data
requires
^{23}
0.4, where
=
_{m} +
_{}.

Some possible pitfalls in this conclusion are that unbiased cluster surveys
have yet to be completed. Use of wide field weak lensing maps will go a
long way towards obtaining a definitive rich cluster sample. There is no
accepted theory for Type Ia supernovae, and it is possible that
evolutionary effects could conspire to produce a dimming that would mimic
the effects of acceleration, at least to *z* ~ 1.
Utilization of supernovae at *z* > 1 will eventually help distinguish
evolutionary dimming or gray dust, the effects of
which should be stronger at earlier epochs and hence
with increasing *z*, from the
effect of acceleration, which decreases at earlier epochs,
that is with increasing *z*.