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Recent years have witnessed a resurgence of interest in the possibility that a positive Lambda-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 Lambda-term. When combined with observations of the cosmic microwave background (CMB), an approximately flat Friedmann-Robertson-Walker (FRW) cosmological model with total energy density (Omegam + OmegaLambda appeq 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 Omegam ltapprox 0.3. In addition, theoretical modelling of structure formation based on the cold dark matter model (CDM) with Omegam = 1 has failed to match up with observations at a quantitative level. By contrast, a flat low density CDM+Lambda universe with Omegam appeq 0.3 and OmegaLambda appeq 0.7, and with an approximately flat (or, Harrison-Zeldovich-like, nS approx 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 Lambda-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 Lambda = 8pi G rhovac / c2 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 rhovac usually appears to be much larger than current observational limits, there is no generic known mechanism which will set the value of Lambda to precisely zero either on the basis of symmetry arguments or by dynamical means. (1) Some recent attempts to generate a small Lambda 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 Lambda-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 Lambda-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| ~ rho c2). 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 Lambda can, of course, be set to zero by hand by adding suitable counterterms to the bare (infinite) value of Lambda 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). Back.

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