Einstein replaced Newton's conception of gravitation as a force with general relativity, which views gravitation as the dynamics of spacetime. In 1917 he applied his theory to the universe as a whole. He made two assumptions: the universe is homogeneous on average and static; and it is closed on itself, a curved volume of space with no boundary. However, Einstein's equations have no such solutions unless an extra term is inserted that acts as a repulsion to offset the gravitational attraction of matter for itself. Thus were born both modern cosmology and the notion of a cosmological constant,

*Lambda*.

In 1929 Hubble found that the universe is expanding, a feature that Friedmann and Lemaître had shown were necessary consequences of Einstein's equations if *Lambda* were zero. There are then three models depending on whether the geometry of space is closed, Euclidean, or open. All three models are characterized by a deceleration in the expansion from a big bang.

Since Hubble's discovery, astronomers have largely focused on determining which of the three Lambda-free models applies on the large scale to the actual universe. Brian Schmidt recognized that white dwarf stars induced to explode as supernovae in galaxies of high expansional redshift *z *constitute a promising luminosity standard with which to measure the geometry of spacetime. In 1994 he formed the High-*z* Supernova Search team to develop this method. They performed the necessary local calibrations and the renormalizations of the different light-curve shapes needed to get accurate results.

Contemporaneously, Saul Perlmutter assumed the leadership of a team that used robotic telescopes to find and characterize supernovae that explode in nearby galaxies. With a redirected effort, the Supernova Cosmology Project automated and brought to maturity the empirical techniques developed by astronomers. The discovery of many supernovae became routine and contributed to the early statistics that the universe may currently be accelerating in its expansion rate, a surprising conclusion reached by the Perlmutter and Schmidt teams simultaneously in 1998.

Adam Riess realized that observations at redshifts *z* larger than readily measurable by telescopes on the ground could eliminate alternative explanations. He led the effort to use the Hubble Space Telescope to find supernovae at z larger than unity. These definitive observations show that supernovae look substantially fainter at large z than predicted by any of the Lambda-free models. Acceleration is required. The best fit for the data is achieved when the current energy-density of the vacuum is about 70% of the critical value that makes the large-scale geometry of space Euclidean, where the last result is suggested by the fluctuations in the microwave background. The corresponding small but nonzero value for the cosmological constant then turns out neatly to resolve the conflict of the universe's age in Euclidean-space models where *Lambda* is set to zero.

The discovery of a non-vanishing energy density of the vacuum, or some more bizarre alternative, has profound consequences for physics, astronomy, and philosophy. It is an accomplishment richly deserving of the Shaw Prize in Astronomy 2006.

Astronomy Selection Committee

The Shaw Prize

12 September 2006, Hong Kong