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 Universe must be $\Omega_0\gtrsim0.7$. Although there are some effects that might weaken this bound, we conclude that open-CDM models with $\Omega_0 \simeq 0.3-0.4$, and the ``open inflation'' theories that produce them, are likely incompatible with CMB/XRB data. This provides additional, albeit indirect, evidence for a cosmological constant.