LARGE-ANGLE COSMIC MICROWAVE BACKGROUND ANISOTROPIES IN AN OPEN UNIVERSE

If the universe is open, scales larger than the curvature scale may be probed by observation of large-angle fluctuations in the cosmic micro wave background (CMB). We consider primordial adiabatic perturbations and discuss power spectra that are power laws in volume, wavelength, a nd eigenvalue of the Laplace operator. Such spectra may have arisen if , for example, the universe underwent a period of ''frustrated'' infla tion. The resulting large-angle anisotropies of the CMB are computed. The amplitude generally increases as OMEGA is decreased but decreases as h is increased. Interestingly enough, for all three Ansatze, anisot ropies on angular scales larger than the curvature scale are suppresse d relative to the anisotropies on scales smaller than the curvature sc ale, but cosmic variance makes discrimination between various models d ifficult. Models with 0.2 less than or similar to OMEGAh less than or similar to 0.3 appear compatible with CMB fluctuations detected by COB E and the Tenerife experiment and with the amplitude and spectrum of f luctuations of galaxy counts in the APM, CfA, and 1.2 Jy IRAS surveys. COBE normalization for these models yields sigma8 congruent-to 0.5-0. 7. Models with smaller values of OMEGAh when normalized to COBE requir e bias factors in excess of 2 to be compatible with the observed galax y counts on the 8 h-1 Mpc scale. Requiring that the age of the univers e exceed 10 Gyr implies that OMEGA greater than or similar to 0.25, wh ile requiring that the age exceed 13 Gyr implies that OMEGA greater th an or similar to 0.35. Unlike in the flat universe case, where the ani stropy comes only from the last-scattering term in the Sachs-Wolfe for mula, large-angle anisotropies come primarily from the decay of potent ial fluctuations at z less than or similar to OMEGA-1. Thus, if the un iverse is open, COBE has been detecting temperature fluctuations produ ced at moderate redshift rather than at z approximately 1300.