**2.2. Possible Kinds of Cosmological Models**

In terms of the parameters *H*,
,
*t*_{glob} and ,
five different combinations are consistent with extant data. The
role of observations is to collapse these five combinations down
to a single on that fits all the data. By convention, instead
of using ,
cosmologists use another parameter
which is just
/
_{c}. A
spatially flat Universe
has = 1. Although many
combinations of these parameters
are allowed, a cosmology in which *H*_{0} is 100,
= 1 and
= 0 produces an expansion
age of only 6.7 Gyrs and
thus can be ruled out. As will be discussed later in this book,
there is strong theoretical prejudice for
= 1 which then
necessarily pushes estimates of *H*_{0} to lower values. Here then
are the current cosmological options which are more or less
consistent with observations:

Option 1:
*H*_{0} is 50,
= 0, the ages of globular clusters are
well understood with *t*_{glob}
16 ± 1 Gyrs, and
0.1 (the Universe is open)
and most of the matter is
baryonic. Arguments for this cosmology were first made in Sandage (1972)
and again most recently in Sandage and Tammann (1997). If this cosmology is
correct, its a nice self-consistent one in which the expansion age
and the globular cluster ages agree. Of course, its difficult to
account for inflation in this model.

Option 2:
*H*_{0} is 100,
= 0, the ages of globular clusters
are at their lowest possible limit, and the Universe must be very open.
The age of the Universe in this cosmology is 10 Gyr. This
option dates back to the work of Gerard De Vaucouleurs in the early 60s
and was strongly revived in the early 80's by the work of
Aaronson et al. (1980, 1985)
Recent improvements in stellar evolutionary code, however, would now seem
to preclude such young globular cluster ages and hence rule out this
cosmology. In addition, other age indicators strongly suggest that the
Galactic Disk is at least 10 Gyrs old. Like option 1, this option is
also inconsistent with the inflationary scenario.

Option 3:
*H*_{0} is 75,
is 0.1 - 0.3, the
ages of globular clusters are marginally understood with
*t*_{glob} in the range 12-15 Gyrs. This is the
compromise option, in which overlapping error bars
accommodate most observations and prejudices, although
= 1 produces an age of only 9 Gyr with this value for *H*_{0}.

Option 4:
*H*_{0} is 50, the Universe is critical
( = 1)
and the ages of globular clusters are marginally understood with
*t*_{glob} being 12-13 Gyr. This option
is preferred by inflationary cosmologies which
predict a critical Universe. This cosmology was strongly favored
in the 1980s to the point that observations which suggested
*H*_{0}
80 were essentially ignored by a
large segment of the
theoretical community since that would conflict with
the = 1 constraint coupled
with the ages of globular clusters.

Option 5: We understand the
ages of globular clusters
with current models putting them at 13-17 billion years. By
the consensus of most of the last 10 years worth of data,
*H*_{0} lies in the range 70-90. Going where this data now leads
then suggests a) the Universe is open or b) the inflationary
constraint of flat space has to be satisfied by a combination of
and
. This option is a
significant departure from
the cosmological models of the 70's and 80's and as we will see later,
has a fair bit of observational support.

Clearly the current situation is unsatisfying as a very large range
of cosmological models remain consistent with the data. As we will
see in Chapter 4, although the inflationary
paradigm is an elegant one,
there is very little observational support for it. At the same time,
there seems to be real conflict between the ages of the oldest stars
and the inferred expansion age based on measurements of *H*_{0}.
We are thus left with either a positive value for
or
a low value for *H*_{0} as the alternatives.