International Journal of Modern Physics D

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.

Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null infinity and the interior region simultaneously (assuming the foliation is free of caustics and crossovers). We discuss how this combination can be performed and illustrate its behavior in the Einstein–Klein–Gordon field in 1D.

The evolution of a causal bulk viscous cosmological fluid filled open conformally flat spacetime is considered. By means of appropriate transformations the equation describing the dynamics and evolution of the very early Universe can be reduced to a first order Abel type differential equation. In the case of a bulk viscosity coefficient proportional to the square root of the density, ξ~ρ^1/2, an exact and two particular approximate solutions are obtained. The resulting cosmologies start from a singular state and generally have a noninflationary behavior, the deceleration parameter tending, in the large time limit, to zero. The thermodynamic consistency of the results is also checked.