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1.4.8 Conclusions Regarding Omega

The main issue that has been addressed so far is the value of the cosmological density parameter Omega. Arguments can be made for Omega0 approx 0.3 (and models such as LambdaCDM; Ch. 4; Ch. 8; Ch. 11) or for Omega = 1 (Section 7; for which the best class of models is probably CHDM), but it is too early to tell which is right.

The evidence would favor a small Omega0 approx 0.3 if: (1) the Hubble parameter actually has the high value H0 approx 75 favored by many observers, and the age of the universe t0 geq 13 Gyr; or (2) the baryonic fraction fb = Mb / Mtot in clusters is actually ~ 15%, about 3 times larger than expected for standard Big Bang Nucleosynthesis in an Omega = 1 universe. This assumes that standard BBN is actually right in predicting that the density of ordinary matter Omegab lies in the range 0.009 leq Omegab h2 leq 0.02. High-resolution, high-redshift spectra are now providing important new data on primordial abundances of the light isotopes that should clarify the reliability of the BBN limits on Omegab. If the systematic errors in the 4He data are larger than currently estimated, then it may be wiser to use the deuterium upper limit Omegab h2 leq 0.03, which is also consistent with the value Omegab h2 approx 0.024 indicated by the only clear deuterium detection at high redshift, with the same D/H approx 2.4 x 10-5 observed in two different low-metallicity quasar absorption systems (Tytler, Fan & Burles 1996); this considerably lessens the discrepancy between fb and Omegab. Another important constraint on Omegab will come from the new data on small angle CMB anisotropies - in particular, the location and height of the first Doppler peak (Dodelson, Gates, & Stebbins 1996; Jungman et al. 1996; Tegmark 1996), with the latest data consistent with low h approx 0.5-0.6 and high Omegab h2 approx 0.025. The location of the first Doppler peak at angular wavenumber l approx 220 indicated by the presently available data (Netterfield et al. 1997, Scott et al. 1996) is evidence in favor of a flat universe; Omega0 ~ 0.3 with Lambda = 0 is disfavored by this data.

The evidence would favor Omega = 1 if: (1) the POTENT analysis of galaxy peculiar velocity data is right, in particular regarding outflows from voids or the inability to obtain the present-epoch non-Gaussian density distribution from Gaussian initial fluctuations in a low-Omega universe; or (2) the preliminary indication of high Omega0 and low OmegaLambda from high-redshift Type Ia supernovae (Perlmutter et al. 1996) is confirmed.

The statistics of gravitational lensing of quasars is incompatible with large cosmological constant Lambda and low cosmological density Omega0. Discrimination between models may improve as additional examples of lensed quasars are searched for in large surveys such as the Sloan Digital Sky Survey. The era of structure formation is another important discriminant between these alternatives, low Omega favoring earlier structure formation, and Omega = 1 favoring later formation with many clusters and larger-scale structures still forming today. A particularly critical test for models like CHDM is the evolution as a function of redshift of Omegagas in damped Lyalpha systems. Reliable data on all of these issues is becoming available so rapidly today that there is reason to hope that a clear decision between these alternatives will be possible within the next few years.

What if the data ends up supporting what appear to be contradictory possibilities, e.g. large Omega0 and large H0? Exotic initial conditions (e.g., ``designer'' primordial fluctuation spectra, cf. Hodges et al. 1990) or exotic dark matter particles beyond the simple ``cold'' vs. ``hot'' alternatives discussed in the next section (e.g., decaying 1-10 MeV tau neutrinos, Dodelson, Gyuk, & Turner 1994; volatile dark matter, Pierpaoli et al. 1996) could increase the space of possible inflationary theories somewhat. But unless new observations, such as the new stellar parallaxes from the Hipparcos satellite, cause the estimates of H0 and t0 to be lowered, it may ultimately be necessary to go outside the framework of inflationary cosmological models and consider models with large scale spatial curvature, with a fairly large Lambda (or non-standard sorts of ``matter'' that violate the strong energy condition - cf. Visser 1997) as well as large Omega0. This seems particularly unattractive, since in addition to implying that the universe is now entering a final inflationary period, it means that inflation probably did not happen at the beginning of the universe, when it would solve the flatness, horizon, monopole, and structure-generation problems. Moreover, aside from the H0 - t0 problem, there is not a shred of reliable evidence in favor of Lambda > 0, just increasingly stringent upper limits. Therefore, most cosmologists are rooting for the success of inflation-inspired cosmologies, with Omega0 + OmegaLambda = 1. With the new upper limits on Lambda from gravitational lensing of quasars, number counts of elliptical galaxies, and high-redshift Type Ia supernovae, this means that the cosmological constant is probably too small to lengthen the age of the universe significantly. So one hopes that when the dust finally settles, H0 and t0 will both turn out to be low enough to be consistent with General Relativistic cosmology. But of course the universe is under no obligation to live up to our expectations.

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