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(o) = 14.0 +/- 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone do not significantly constrain either h or Omega (Lambda). This small uncertainty is due to the tight (and accidental) correlation in flat adiabatic 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 Hubble Space Telescope Key Project result h = 0.72 +/- 0.08 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.