Open Cold Dark Matter Models

TL;DR

This paper evaluates open cold dark matter models against various cosmological observations, finding that models with certain density parameters and Hubble constants can fit the data, especially when considering spectral index variations.

Contribution

It provides a comprehensive comparison of open CDM models with observational data, including new treatments for damped Lyman alpha systems in open universes.

Findings

Good fit for .35 .55 with arbitrary Hubble parameter

Models with .35 .55 fit data if H > 0.6

Allowed .30 to .60 for spectral index 0.9 to 1.1

Abstract

Motivated by recent developments in inflationary cosmology indicating the possibility of obtaining genuinely open universes in some models, we compare the predictions of cold dark matter (CDM) models in open universes with a variety of observational information. The spectrum of the primordial curvature perturbation is taken to be scale invariant (spectral index $n=1$), corresponding to a flat inflationary potential. We allow arbitrary variation of the density parameter $\Omega_0$ and the Hubble parameter $h$, and take full account of the baryon content assuming standard nucleosynthesis. We normalize the power spectrum using the recent analysis of the two year {\it COBE} DMR data by G\'{o}rski et al. We then consider a variety of observations, namely the galaxy correlation function, bulk flows, the abundance of galaxy clusters and the abundance of damped Lyman alpha systems. For the last two of these, we provide a new treatment appropriate to open universes. We find that, if one allows an arbitrary $h$, then a good fit is available for any $\Omega_0$ greater than 0.35, though for $\Omega_0$ close to 1 the required $h$ is alarmingly low. Models with $\Omega_0 < 0.35$ seem unable to fit observations while keeping the universe over $10$ Gyr old; this limit is somewhat higher than that appearing in the literature thus far. If one assumes a value of $h > 0.6$, as favoured by recent measurements, concordance with the data is only possible for the narrow range $0.35 < \Omega_0 < 0.55$. We have also investigated $n \neq 1$; the extra freedom naturally widens the allowed parameter region. Assuming a range $0.9<n<1.1$, the allowed range of $\Omega_0$ assuming $h > 0.6$ is at most $0.30 < \Omega_0 < 0.60$.