Correlations Between the Cosmic X-ray and Microwave Backgrounds: Constraints on a Cosmological Constant

In universes with significant curvature or cosmological constant, cosmic microwave background (CMB) anisotropies are created very recently via the Rees-Sciama or integrated Sachs-Wolfe effects. This causes the CMB anisotropies to become partially correlated with the local matter density (z < 4). We examine the prospects of using the hard (2-10 keV) X-ray background as a probe of the local density and the measured correlation between the HEAO1 A2 X-ray survey and the 4-year COBE-DMR map to obtain a constraint on the cosmological constant. The 95% confidence level upper limit on the cosmological constant is \Omega_\Lambda \leq 0.5, assuming that the observed fluctuations in the X-ray map result entirely from large scale structure. (This would also imply that the X-rays trace matter with a bias factor of b_x = 5.6 \Omega_m^{0.53}.) This bound is weakened considerably if a large portion of the X-ray fluctuations arise from Poisson noise from unresolved sources. For example, if one assumes that the X-ray bias is b_x = 2., then the 95% confidence level upper limit is weaker, \Omega_\Lambda \leq 0.7. More stringent limits should be attainable with data from the next generation of CMB and X-ray background maps.