Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue on Dark Energ

Stable gravastars with generalised exteriors

New spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti--de Sitter or de Sitter interior and a Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviours of the equation of state for these parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit

Where are all the gravastars? Limits upon the gravastar model from accreting black holes

The gravastar model, which postulates a strongly correlated thin shell of anisotropic matter surrounding a region of anti-de Sitter space, has been proposed as an alternative to black holes. We discuss constraints that present-day observations of well-known black hole candidates place on this model. We focus upon two black hole candidates known to have extraordinarily low luminosities: the supermassive black hole in the Galactic Center, Sagittarius A*, and the stellar-mass black hole, XTE J1118+480. We find that the length scale for modifications of the type discussed in Chapline et al. (2003) must be sub-Planckian.Comment: 11 pages, 4 figure

Gravastar Solutions with Continuous Pressures and Equation of State

We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.Comment: 19 pages, 9 figures. Latest version contains new and updated references along with some clarifying remarks in the stability analysi

Quantum Diffeomorphisms and Conformal Symmetry

We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe $R \times S^3$. The $SO(4,2)$ global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equation is {\it modified} at the quantum level in a well-defined way in this case. We argue that the higher moments of $T^{00}$ should not be imposed on the physical states {\it a priori} either, but only the weaker condition $\langle \dot T^{00} \rangle = 0$. We present an explicit example of the quantization and diffeomorphism constraints on $R \times S^3$ for a free conformal scalar field.Comment: PlainTeX File, 37 page

Gravastars must have anisotropic pressures

One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the "gravastar" model developed by Mazur and Mottola; and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure -- without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluids -- anisotropic pressures in the "crust" of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation.Comment: V1: 15 pages; 4 figures; uses iopart.cls; V2: 16 pages; added 3 references and brief discussio

Gravity a la Born-Infeld

A simple technique for the construction of gravity theories in Born-Infeld style is presented, and the properties of some of these novel theories are investigated. They regularize the positive energy Schwarzschild singularity, and a large class of models allows for the cancellation of ghosts. The possible correspondence to low energy string theory is discussed. By including curvature corrections to all orders in alpha', the new theories nicely illustrate a mechanism that string theory might use to regularize gravitational singularities.Comment: 21 pages, 2 figures, new appendix B with corrigendum: Class. Quantum Grav. 21 (2004) 529

De Sitter Waves and the Zero Curvature Limit

We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far as one wishes to recover ordinary QFT in the flat limit.Comment: 9 pages, latex no figure, to appear in Phys. Rev.