Type Ia supernovae and cosmology

The direct evidence for the acceleration of the local Universe away from a matter-dominated frame rests on a simple observational result: the Type Ia supernovae at z similar to 0.5 are about 0.25 magnitude too faint relative to a matter dominated universe with (Omega(M), Omega(Lambda)) = (0.3, 0.0). We choose to interpret our observations in a simple fashion: the faintness of the supernovae is due to increased luminosity distances to the supernovae. In turn, the increased size of the local Universe can be interpreted as the effect of the cumulative repulsion from a dark energy associated with the cosmological constant of Einstein. In this short summary, I will explore the technique for the measurement of luminosities distances using SNe Ia, and some of the underlying assumptions we have made.