### IV. THE COSMOLOGICAL TESTS

Our intention is to supplement recent discussions of parameter
determinations within the standard relativistic cosmology
^{58} with a broader
consideration of the issues summarized in two
questions: what is the purpose of the cosmological tests, and how
well is the purpose addressed by recent advances and work in progress?

The short answer to the first question used to be that we seek to
check the underlying physical theory, general
relativity, applied on the time and length scales of cosmology;
the model for the stress-energy tensor in Einstein's field
equation, suitably averaged over the rich small-scale structure
we cannot describe in any detail; and the boundary condition,
that the universe we can observe is close to homogeneous and
isotropic on the scale of the Hubble length. Recent advances make
use of the CDM prescription for the stress-energy tensor and the
boundary condition, so we must add the elements of the CDM model
to the physics to be checked.

The short answer to the second question is that we now have
searching checks of the standard cosmology, which the
model passes. But we believe it takes nothing away from the
remarkable advances of the tests, and the exemplary care in the
measurements, to note that there is a lot of room for
systematic errors. As we discussed in
Sec. I.A, the empirical
basis for the standard model for cosmology is not nearly as
substantial as is the empirical basis for the standard model for
particle physics: in cosmology it is not yet a matter of
measuring parameters in a well-established physical theory.

We comment on the two main pieces of physics, general relativity
and the CDM model, in Secs. IV.A.1
and IV.A.2. In
Sec. IV.B we discuss the state of 13
cosmological tests,
proceeding roughly in order of increasing model dependence. We
conclude that there is a well-established scientific case for the
physical significance of the matter density parameter, and for
the result of the measurements,
0.15
_{M0}
0.4 (in the
sense of a two standard deviation range). Our reasoning is
summarized in Sec. IV.C, along with an
explanation of why we are not so sure about the detection of
or dark energy.

^{58} See
Bahcall et al. (1999),
Schindler (2001),
Sarkar (2002),
Freedman (2002),
Plionis (2002),
and references therein.
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