High Redshift Supernovae: Cosmological Implications

We review the findings for the values of the cosmological parameters as derived from high-redshift SNIa measurements. The most recent results confirm the picture of a non-empty inflationary Universe that is consistent with a cosmological constant Omega_Lambda~0.7. This implies that the expansion of the Universe is currently accelerated by the action of some mysterious dark energy. We also discuss the possibility and the consequences of the fact that SNIa may not be "perfect" standard candles, in the sense of having properties in the early Universe that are systematically different from those they have at the present times.