The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements

If Omega_tot = 1 and structure formed from adiabatic initial conditions then the age of the Universe, as constrained by measurements of the cosmic microwave background (CMB), is t_0=14.0 +/- 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone constrain neither h nor Omega_Lambda significantly. It is due to the tight (and accidental) correlation, in these models, of the age with the angle subtended by the sound horizon on the last–scattering surface and thus with the well-determined acoustic peak locations. If we assume either the HST Key Project result h = 0.72 \pm .08 or simply that h > 0.55, we find Omega_Lambda > 0.4 at 95% confidence–another argument for dark energy, independent of supernovae observations. Our analysis is greatly simplified by the Monte Carlo Markov chain approach to Bayesian inference combined with a fast method for calculating angular power spectra.