Dark matter and cosmology: CDM with a cosmological constant (ACDM) vs CDM with hot dark matter (CHDM)

The fact that the simplest modern cosmological theory, standard Cold Dark Matter (sCDM), almost fits all available data has encouraged the search for variants of CDM that can do better. Here we discuss what are perhaps the two most popular variants of CDM that might agree with the data: Lambda CDM and CHDM. While the predictions of COBE-normalized Lambda CDM and CHDM both agree well with the available data on scales of similar to 10 to 100 h(-1) Mpc, each has potential virtues and defects. Lambda CDM with Omega(0) similar to 0.3 has the possible virtue of allowing a higher expansion rate H-0 for a given cosmic age t(0), but the defect of predicting too much fluctuation power on small scales. CHDM has less power on small scales, so its predictions appear to be in good agreement with data on the galaxy distribution, but it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. Also, several sorts of data suggest that neutrinos have nonzero mass. And two very recent observational results favor high cosmic density, and thus favor Omega = 1 models such as CHDM over Lambda CDM - (1) the positive deceleration parameter q(0) > 0 measured using high-redshift Type 1a supernovae, and (2) the low primordial deuterium/hydrogen ratio measured in two different quasar absorption spectra. If confirmed, (1) rules out a cosmological constant large enough to help significantly with the He-to problem; while (2) suggests that the baryonic cosmological density is at the upper end of the range allowed by Big Bang Nucleosynthesis, perhaps high enough to resolve the ''cluster baryon crisis'' for Omega = I models. We try to identify ''best'' variants of both Lambda CDM and CHDM, and discuss critical observational tests for both models.