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2.2. Possible Kinds of Cosmological Models

In terms of the parameters H, rho, tglob and Lambda, 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 rho, cosmologists use another parameter Omega which is just rho / rhoc. A spatially flat Universe has Omega = 1. Although many combinations of these parameters are allowed, a cosmology in which H0 is 100, Omega = 1 and Lambda = 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 Omega = 1 which then necessarily pushes estimates of H0 to lower values. Here then are the current cosmological options which are more or less consistent with observations:

bullet Option 1: H0 is 50, Lambda = 0, the ages of globular clusters are well understood with tglob approx 16 ± 1 Gyrs, and Omega approx 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.

bullet Option 2: H0 is 100, Lambda = 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.

bullet Option 3: H0 is 75, Omega is 0.1 - 0.3, the ages of globular clusters are marginally understood with tglob in the range 12-15 Gyrs. This is the compromise option, in which overlapping error bars accommodate most observations and prejudices, although Omega = 1 produces an age of only 9 Gyr with this value for H0.

bullet Option 4: H0 is 50, the Universe is critical (Omega = 1) and the ages of globular clusters are marginally understood with tglob 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 H0 geq 80 were essentially ignored by a large segment of the theoretical community since that would conflict with the Omega = 1 constraint coupled with the ages of globular clusters.

bullet 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, H0 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 Omega and Lambda. 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 H0. We are thus left with either a positive value for Lambda or a low value for H0 as the alternatives.

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