Recent years have witnessed a resurgence of interest in the possibility that a positive -term (a cosmological constant) may dominate the total energy density in the universe. Interest in the cosmological constant stems from several directions:

(i) Observations of high redshift Type 1a supernovae appear to suggest
that our universe may be accelerating with a large fraction of the
cosmological density in the form of a cosmological
-term. When combined
with observations of the cosmic microwave background (CMB), an approximately
flat Friedmann-Robertson-Walker (FRW) cosmological model with
total energy density
(_{m} +
_{}
1) is suggested, in
agreement
with predictions of the simplest versions of the inflationary scenario
of the early universe (sections 4.3,
4.4).

(ii) Most dynamical estimates of the amount of clustered matter yield a
conservative upper limit
_{m}
0.3. In addition,
theoretical modelling
of structure formation based on the cold dark matter model (CDM) with
_{m} = 1 has
failed to match up with observations at a quantitative
level. By contrast, a flat low density
CDM+ universe with
_{m}
0.3 and
_{}
0.7, and with an
approximately flat (or, Harrison-Zeldovich-like,
*n*_{S}
1) initial Fourier spectrum of
scalar (adiabatic) inhomogeneous metric and density perturbations agrees
remarkably well with a wide range of observational
data ranging from large and intermediate angle CMB anisotropies to
observations of galaxy clustering on large scales. Since an
approximately flat initial spectrum of adiabatic perturbations is also
precisely what simplest variants of the inflationary scenario predict,
the positive -term
removes a necessity in any complications of
the inflationary scenario (which might be required if the
universe was found to be open).

(iii) At a theoretical level, a cosmological constant
=
8 *G*
_{vac}
/ *c*^{2} is predicted to arise out of zero-point quantum
vacuum fluctuations
of fundamental scalar, spinor, vector and tensor fields (see
section 5).
Although a theoretically predicted value of
_{vac}
usually appears to be
much larger than current observational
limits, there is no generic known mechanism which will set the value of
to precisely zero
either on the basis of symmetry arguments
or by dynamical means. ^{(1)}
Some recent attempts to generate a small
at the present
epoch either through vacuum polarization and particle creation effects
or by means of dynamically evolving scalar fields
are discussed in section 7.

Although none of the above arguments can by themselves be regarded as conclusive evidence for a cosmological constant, the growing body of work on the subject, combined with a possible deep relationship between a small cosmological constant today and a large cosmological term driving inflation at an early epoch, suggests that the case for a positive cosmological constant be taken seriously. In this paper we attempt to review some aspects of the cosmological constant issue emphasizing both theoretical as well as observational aspects. For earlier reviews on the subject the reader is referred to Zeldovich (1968), Weinberg (1989) and Caroll, Press and Turner (1992).

From the physical point of view, a
-term represents a new
type of dark non-baryonic matter, completely unknown from laboratory
experiments. Its difference from another type of dark non-baryonic
matter that has been already introduced in cosmology for almost two decades
from observations of gravitational clustering is essentially that matter
described by the
-term is, (a) not
gravitationally clustered at all
scales at which we see clustering of baryons and dustlike dark matter, and
(b) has a strongly negative effective pressure
(*P* < 0, |*P*| ~
*c*^{2}).
Thus, remarkably, by investigating the behaviour of the present universe
we are studying novel fundamental physics. Extragalactic astronomy and
cosmology once more become a driving force for new insights in physics !

^{1} The value of
can, of course,
be set to zero by hand by adding
suitable counterterms to the bare (infinite) value of
in the Lagrangian.
This method, however, amounts to a rather ad-hoc adjustment of
parameters and cannot be regarded as being `generic'
(see section 5).
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