The present author, like many theorists, has long regarded the
Einstein-de Sitter
(_{m} = 1,
= 0) cosmology as the most
attractive one. For one thing, there are only three possible constant
values for - 0, 1, and
- of which the only one
that can describe our universe is
_{m} = 1. Also, cosmic
inflation is the only known solution for several otherwise intractable
problems, and all simple inflationary models predict that the universe
is flat, i.e. that
_{m}
+ _{} = 1. Since there is no
known physical reason for a non-zero cosmological constant, it was
often said that inflation favors
= 1. Of course, theoretical
prejudice is not a reliable guide. In recent years, many cosmologists
have favored _{m} ~
0.3, both because of the *H*_{0} - *t*_{0}
constraints and because cluster and other relatively small-scale
measurements have given low values for
_{m}. (For a summary of
arguments favoring low
_{m}
0.2 and
= 0, see
Coles & Ellis (1997).
A review that notes that larger scale
measurements favor higher
_{m} is
Dekel, Burstein, & White
1997.)
But the most exciting new evidence has come from
cosmological-scale measurements.

**Type Ia Supernovae.** At present, the most promising techniques
for measuring _{m} and
_{} on cosmological scales
use the small-angle anisotropies in the CMB radiation and
high-redshift Type Ia supernovae (SNe Ia). We will discuss the latter
first. SNe Ia are the brightest supernovae, and the spread in their
intrinsic brightness appears to be relatively small. The Supernova
Cosmology Project
(Perlmutter et al. 1997a)
demonstrated the
feasibility of finding significant numbers of such supernovae. The
first seven high redshift SNe Ia that they analyzed gave for a flat
universe _{m} = 1 -
_{} =
0.94^{+0.34}_{-0.28}, or equivalently
_{} =
0.06^{+0.28}_{-0.34} (< 0.51 at the 95% confidence level)
(Perlmutter et al. 1997a).
But adding one
*z* = 0.83 SN Ia for which they had good HST data lowered the implied
_{m} to 0.6 ± 0.2
in the flat case
(Perlmutter et al. 1998).
Analysis of their larger dataset of 42 high-redshift SNe Ia gives for
the flat cast _{m} =
0.28^{+0.09 +0.05}_{-0.08 -0.04} where the
first errors are statistical and the second are identified systematics
(Perlmutter et al. 1999).
The High-Z Supernova team has also searched
successfully for high-redshift supernovae to measure
_{m}
(Garnavich et al. 1997,
Riess et al. 1998),
and their three HST SNe
Ia, two at *z* 0.5 and
one at 0.97, imply _{m}
= 0.4 ±
0.3 in the flat case. The main concerns about the interpretation of
this data are evolution of the SNe Ia
(Drell, Loredo, &
Wasserman 1999)
and dimming by dust. A recent specific supernova evolution
concern that was discussed at this workshop is that the rest frame
rise-times of distant supernovae may be longer than nearby ones
(Riess et al. 1999).
But a direct comparison between nearby supernova and
the SCP distant sample shows that they are rather consistent with each
other
(Aldering, Nugent, &
Knop 1999).
Ordinary dust causes
reddening, but hypothetical grey dust would cause much less reddening
and could in principle provide an alternative explanation for the fact
that high-redshift supernovae are observed to be dimmer than expected
in a critical-density cosmology. It is hard to see why the largest
dust grains, which would be greyer, should preferentially be ejected
by galaxies
(Simonsen & Hannestad
1999).
Such dust, if it exists,
would also absorb starlight and reradiate it at long wavelengths,
where there are other constraints that could, with additional
observations, rule out this scenario
(Aguirre & Haiman 1999).
But another way of addressing this question is to collect data on
supernovae with redshift *z* > 1, where the dust scenario predicts
considerably more dimming than the
cosmology.
The one *z* > 1 supernova currently available, SCP's ``Albinoni''
(SN1998eq) at *z* = 1.2, will help, and both the SCP and the High-Z
group are attempting to
get a few more very high redshift supernovae.

**CMB anisotropies.** The location of the first Doppler (or
acoustic, or Sakharov) peak at angular wavenumber *l*
250
indicated by the presently available data (Scott, this volume) is
evidence in favor of a flat universe
_{m} +
_{}
1. New data from the MAXIMA
and BOOMERANG balloon flights
apparently confirms this, and the locations of the second and
possibly third peak appear to be consistent with the predictions
(Hu, Spergel, & White 1997)
of simple cosmic inflation theories. Further
data should be available in 2001 from the NASA Microwave Anisotropy
Probe satellite.

**Large-scale Measurements.** The comparison of the IRAS redshift
surveys with POTENT and related analyses typically give values for the
parameter
_{I}
_{m}^{0.6} /
*b*_{I} (where *b*_{I} is the
biasing parameter for IRAS galaxies), corresponding to
0.3
_{m}
3 (for an assumed
*b*_{I} = 1.15). It is not clear
whether it will be possible to reduce the spread in these values
significantly in the near future - probably both additional data and
a better understanding of systematic and statistical effects will be
required. A particularly simple way to deduce a lower limit on
_{m} from the POTENT
peculiar velocity data was proposed by
Dekel & Rees (1994),
based on the fact that high-velocity outflows
from voids are not expected in
low- models. Data on just one
nearby void indicates that
_{m}
0.3 at the 97% C.L.
Stronger constraints are available if we assume that the probability
distribution function (PDF) of the primordial fluctuations was
Gaussian. Evolution from a Gaussian initial PDF to the non-Gaussian
mass distribution observed today requires considerable gravitational
nonlinearity, i.e. large
_{m}. The PDF deduced
by POTENT from
observed velocities (i.e., the PDF of the mass, if the POTENT
reconstruction is reliable) is far from Gaussian today, with a long
positive-fluctuation tail. It agrees with a Gaussian initial PDF if
and only if _{m} ~
1; _{m} < 1 is rejected at the
2 level, and
_{m}
0.3 is ruled out at
4
(Nusser & Dekel 1993; cf.
Bernardeau et al. 1995).
It would be
interesting to repeat this analysis with newer data.

**Measurements on Scales of a Few Mpc.** A study by the Canadian
Network for Observational Cosmology (CNOC) of 16 clusters at *z* ~
0.3, mostly chosen from the Einstein Medium Sensitivity Survey
(Henry et al. 1992),
was designed to allow a self-contained measurement of
_{m} from a field *M
/ L* which in turn was deduced from their
measured cluster *M / L*. The result was
_{m} = 0.19 ± 0.06
(Carlberg et al. 1997).
These data were mainly compared to
standard CDM models, and they appear to exclude
_{m} = 1 in such models.

**Estimates on Galaxy Halo Scales.** Work by
Zaritsky et al. (1993)
has confirmed that spiral galaxies have massive halos. They collected
data on satellites of isolated spiral galaxies, and concluded that the
fact that the relative velocities do not fall off out to a separation
of at least 200 kpc shows that massive halos are the norm. The
typical rotation velocity of ~ 200-250 km s^{-1} implies a mass
within 200 kpc of ~ 2 x 10^{12}
*M*_{}. A careful analysis
taking into account selection effects and satellite orbit
uncertainties concluded that the indicated value of
_{m} exceeds
0.13 at 90% confidence
(Zaritsky & White 1994),
with preferred
values exceeding 0.3. Newer data suggesting that relative velocities
do not fall off out to a separation of ~ 400 kpc
(Zaritsky et al. 1997)
presumably would raise these
_{m} estimates.

**Cluster Baryons vs. Big Bang Nucleosynthesis.**
White et al. (1993)
emphasized that X-ray observations of the abundance of baryons
in clusters can be used to determine
_{m} if clusters are a fair
sample of both baryons and dark matter, as they are expected to be
based on simulations
(Evrard, Metzler, &
Navarro 1996).
The fair sample hypothesis implies that

(1) |

We can use this to determine
_{m} using the baryon
abundance _{b}
*h*^{2} = 0.019 ± 0.001 from the measurement of the deuterium
abundance in high-redshift Lyman limit systems, of which a third has
recently been discovered
(Kirkman et al. 1999).
Using X-ray data from an
X-ray flux limited sample of clusters to estimate the baryon fraction
*f*_{b} = 0.075 *h*^{-3/2}
(Mohr, Mathiesen, &
Evrard 1999)
gives _{m} = 0.25
*h*^{-1/2} = 0.3 ± 0.1 using *h* = 0.65 ± 0.08.
Estimating the baryon fraction using Sunyaev-Zel'dovich measurements
of a sample of 18 clusters gives *f*_{b} = 0.77
*h*^{-1}
(Carlstrom et al. 1999),
and implies _{m} = 0.25 *h*^{-1} = 0.38 ± 0.1.

**Cluster Evolution.** The dependence of the number of clusters on
redshift can be a useful constraint on theories (e.g.,
Eke et al. 1996).
But the cluster data at various redshifts are difficult to
compare properly since they are rather inhomogeneous. Using just
X-ray temperature data,
Eke et al. (1998)
conclude that _{m}
0.45 ± 0.2, with
_{m} = 1 strongly disfavored.

**Power Spectrum.** In the context of the
CDM class of models,
two additional constraints are available. The spectrum shape
parameter
_{m} *h*
0.25 ± 0.05, implying
_{m}
0.4 ± 0.1. A new
measurement _{m} = 0.34
± 0.1
comes from the amplitude of the power spectrum of fluctuations at
redshift *z* ~ 3, measured from the Lyman
forest
(Weinberg et al. 1999).
This result is strongly inconsistent with
high-_{m} models
because they would predict that the
fluctuations grow much more to *z* = 0, and thus would be lower at
*z* = 3 than they are observed to be.