A New Constraint to Open Cold-Dark-Matter Models

We calculate the large-angle cross-correlation between the cosmic-microwave-background (CMB) temperature and the x-ray-background (XRB) intensity expected in an open Universe with cold dark matter (CDM) and a nearly scale-invariant spectrum of adiabatic density perturbations. Using a recent experimental upper limit to the amplitude of this cross-correlation, we find that the matter density (in units of the critical density) in an open-CDM model must be $\Omega_0\gtrsim0.7$. We discuss several effects that might change this bound, especially the possible contribution of Poisson fluctuations in the XRB. Although loopholes may allow a lower density, a value $\Omega_0 \simeq 0.3-0.4$, is certainly easier to accommodate in a cosmological-constant Universe than in an open Universe.