3. INFLATION + CDM IN THE ERA OF PRECISION COSMOLOGY
As we look forward to the abundance (avalanche!) of highquality
observations
that will test Inflation + CDM, we have to make sure the predictions
of the theory match the precision of the data. In
so doing, CDM + Inflation becomes a ten (or more) parameter
theory. For astrophysicists, and especially cosmologists,
this is daunting, as it may seem that a tenparameter
theory can be made to fit any set of observations. This is
not the case when one has the quality and quantity of data
that will be coming. The standard model of particle physics offers
an excellent example: it is
a nineteenparameter theory and because of the highquality of
data from experiments at Fermilab's Tevatron, SLAC's SLC,
CERN's LEP and other facilities it has been rigorously tested
and the parameters measured to a precision of better than 1%
in some cases. My worry as an inflationist is not that many different
sets of parameters will fit the upcoming data, but rather that
no set of parameters will!
In fact, the ten parameters of CDM + Inflation
are an opportunity rather than a curse: Because the parameters
depend upon the underlying inflationary model and fundamental
aspects of the Universe, we have the very real possibility of learning
much about the Universe and inflation. The ten parameters
can be organized into two groups: cosmological and darkmatter
(Dodelson et al, 1996).
Cosmological Parameters
 h, the Hubble constant in units of
100 km s^{1} Mpc^{1}.

_{B}
h^{2}, the baryon density. Primeval deuterium
measurements and together with the theory of BBN imply:
_{B}
h^{2} = 0.02 ± 0.002.
 n, the powerlaw index of the scalar density perturbations.
CBR measurements indicate
n = 1.1 ± 0.2; n = 1 corresponds to
scaleinvariant density perturbations. Several popular
inflationary models predict
n 0.95; range of
predictions runs from 0.7 to 1.2
(Lyth & Riotto, 1996).
 dn / dln k, "running" of the scalar index with
comoving scale
(k = wavenumber). Inflationary models predict a value of
( ±
10^{3}) or smaller
(Kosowsky & Turner,
1995).
 S, the overall amplitude squared of density perturbations,
quantified by their contribution to the variance of the
CBR quadrupole anisotropy.
 T, the overall amplitude squared of gravity waves,
quantified by their contribution to the variance of the
CBR quadrupole anisotropy. Note, the COBE normalization determines
T + S (see below).
 n_{T}, the powerlaw index of the gravity wave spectrum.
Scaleinvariance corresponds to n_{T} = 0; for inflation,
n_{T} is given by  1/7 T/S.
Darkmatter Parameters

_{}, the fraction of critical
density in neutrinos
(= _{i}
m_{i} /
90h^{2}). While the hot dark matter theory of structure
formation is not viable, it is possible that a small fraction of
the matter density exists in the form of neutrinos.
Further, small  but nonzero  neutrino masses are
a generic prediction of theories that unify the
strong, weak and electromagnetic interactions  and the
SuperKamiokande Collaboration has presented
evidence that the at least one of the neutrino species has a
mass of greater than about 0.1eV, based upon the deficit
of atmospheric muon neutrinos
(Fukuda et al, 1998).
 _{X}, the
fraction of critical density in a smooth component
of unknown composition and negative pressure
(w_{X}
 0.3). There is
mounting evidence for such a component, with the simplest example being
a cosmological constant (w_{X} =  1).
 g_{*}, the quantity that counts the number of
ultrarelativistic
degrees of freedom (around the time of matterradiation
equality). The standard cosmology/standard
model of particle physics predicts
g_{*} = 3.3626 (photons in the
CBR + 3 massless neutrino species with temperature (4/11)^{1/3}
times that of the photons). The amount of radiation controls when
the Universe became matter dominated and thus affects the present
spectrum of density inhomogeneity.
3.1. Present status of Inflation + CDM
A useful way to organize the different CDM models is by their
darkmatter content; within each CDM family, the cosmological
parameters vary. One list of models is:
 sCDM (for simple): Only CDM and baryons; no additional
radiation (g_{*} = 3.36). The original standard
CDM is a member
of this family (h = 0.50, n = 1.00,
_{B} = 0.05), but is
now ruled out (see Fig. 3).
 CDM: This model has
extra radiation, e.g., produced by the decay of an unstable
massive tau neutrino (hence the name); here we take
g_{*} = 7.45.
 CDM (for neutrinos): This model has a dash of hot
dark matter; here we take
_{} = 0.2 (about 5eV
worth of neutrinos).
 CDM (for cosmological constant): This model has
a smooth component in the form of a cosmological constant; here
we take
_{} = 0.6.

Figure 3. Summary of viable CDM models,
based upon CBR anisotropy and determinations of the present
power spectrum of inhomogeneity
(Dodelson et al, 1996).

Figure 3 summarizes the viability of these
different CDM models,
based upon CBR measurements and current determinations of
the present power spectrum of inhomogeneity derived from
redshift surveys. sCDM is only viable for low values of the
Hubble constant (less than
55 km s^{1} Mpc^{1}) and/or
significant tilt (deviation from scale invariance); the region
of viability for CDM is similar
to sCDM, but shifted
to larger values of the Hubble constant (as large as
65 km s^{1} Mpc^{1}). CDM has an island of viability
around
H_{0} ~ 60 km s^{1} Mpc^{1} and
n ~ 0.95. CDM
can tolerate the largest values of the Hubble constant.
Considering other relevant data too  e.g.,
age of the Universe, determinations of
_{M},
measurements of the Hubble constant, and limits to
_{}  CDM emerges as the
"bestfit CDM model"
(Krauss & Turner,
1995;
Ostriker & Steinhardt,
1995;
Liddle et al, 1996);
see Fig. 4.
Moreover, its "smoking gun signature,"
negative q_{0}, has apparently been confirmed
(Riess et al, 1998;
Perlmutter et al, 1998).
Despite my general
enthusiasm, I would caution that it is premature
to conclude that CDM is anything but the model
to take aim at.