1. INTROUCTION

Einstein (1917) introduced the cosmological constant because he believed that a closed static universe which emerged in the presence of both and matter agreed with Ernst Mach's concepts of inertia [1, 2] which forbade the notion of `empty space'. However, the discovery by Friedmann (1922) of expanding solutions to the Einstein field equations in the absence of , together with the discovery by Hubble (1929) that the universe was expanding, gave a blow to the static model [3, 4]. Soon after, Einstein discarded the cosmological constant. Although abandoned by Einstein, the cosmological constant staged several come-backs. It was soon realised that, since the static Einstein universe is unstable to small perturbations, one could construct expanding universe models which had a quasi-static origin in the past, thus ameliorating the initial singularity which plagues expanding FRW models. One could also construct models which approached the static Einstein universe during an intermediate epoch when the universe `loitered' with a constant. Such a model was proposed by Lemaitre (1927) and was to prove influential later, in 1968, when it was invoked to explain an alleged excess of quasars at a redshift z ~ 2. It is also interesting that during the very same year that Einstein proposed the cosmological constant, de Sitter discovered a matter-free solution to the Einstein equations in the presence of , which had both static and dynamic representations. The de Sitter metric was to play an important role both in connection with steady state cosmology as well as in the construction of inflationary models of the very early universe.

A physical basis for the cosmological constant had to wait until 1968, when Ya. B. Zel'dovich puzzling over cosmological observations which appeared to require (the quasar excess at z ~ 2 alluded to earlier) realised that one loop quantum vacuum fluctuations ⁽¹⁾ gave rise to an energy momentum tensor which, after being suitably regularised for infinities, had exactly the same form as a cosmological constant: <T_ik>_vac = g_ik / 8G.

Theoretical interest in remained on the increase during the 1970's and early 1980's with the construction of inflationary models, in which matter (in the form of a false vacuum, as vacuum polarization or as a minimally coupled scalar-field) behaved precisely like a weakly time-dependent -term. The current interest in stems mainly from observations of Type Ia high redshift supernovae which indicate that the universe is accelerating fueled perhaps by a small cosmological -term [10, 11]. ⁽²⁾

¹ The presence of zero-point vacuum fluctuations was predicted by Casimir [8] and has been verified by several experiments, see [9] and references therein. Back.

² The chronology of interest in bears a curious historical parallel to the scientific fascination with the notion of extra dimensions. (I thank Nathalie Duruelle for an interesting discussion on this issue during the meeting.) A fourth spatial dimension was proposed by Nordström (1914) and independently by Kaluza (1921), but the real scientific interest in higher dimensions grew after de Witt (1962), Kerner (1968) and others [16] had convincingly demonstrated the deep relationship between higher dimensional theories on the one hand, and non-abelian gauge fields on the other. Cosmology in a space-time with extra dimensions really took off during the 1970's and early 1980's when grand unified and supergravity models frequently relied on compact extra dimensions to generate the extra gauge degrees of freedom associated with unification. Current interest in higher dimensional cosmologies is spurred by superstring theory as well as by `brane-world' scenario's of extra dimensions. Back