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} /
8*G*.

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.
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