Weighing the Universe with the Cosmic Microwave Background

Variations in $\Omega$, the total density of the Universe, leave a clear and distinctive imprint on the power spectrum of temperature fluctuations in the cosmic microwave background (CMB). This signature is virtually independent of other cosmological parameters or details of particular cosmological models. We evaluate the precision with which $\Omega$ can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size. For example, assuming only that the primordial density perturbations were adiabatic and with no prior information on the values of any other cosmological parameters, a full-sky CMB map at $0.5^\circ$ angular resolution and a noise level of $15\,\mu{\rm K}$ per pixel can determine $\Omega$ with a variance of 5\%. If all other cosmological parameters are fixed, $\Omega$ can be measured to better than 1\%.