Quantum vacuum fluctuations and dark energy

It is shown that the curvature of space-time induced by vacuum fluctuations of quantum fields should be proportional to the square of Newton's constant $G$. This offers a possible explanation for the success of the approximation $G m^6 c^2 h^{-4}$ for the dark energy density, with $m$ being a typical mass of elementary particles.Comment: Changed conten

Universality and Critical Phenomena in String Defect Statistics

The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, and for cosmic strings, where the proportion of infinite strings can be varied or disappear entirely depending on the bias in the symmetry. In this paper we measure the initial configurational statistics of a network of string defects after a symmetry-breaking phase transition with initial bias in the symmetry of the ground state. Using an improved algorithm, which is useful for a more general class of self-interacting walks on an infinite lattice, we extend the work in \cite{MHKS} to better statistics and a different ground state manifold, namely $\R P^2$, and explore various different discretisations. Within the statistical errors, the critical exponents of the Hagedorn transition are found to be quite possibly universal and identical to the critical exponents of three-dimensional bond or site percolation. This improves our understanding of the percolation theory description of defect statistics after a biased phase transition, as proposed in \cite{MHKS}. We also find strong evidence that the existence of infinite strings in the Vachaspati Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included. also available on http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g

Dark energy as a curvature of space-time induced by quantum vacuum fluctuations

It is shown that quantum vacuum fluctuations give rise to a curvature of space-time of the order appropriate to explain the observed accelerated expansion of the universe. The fact that the fluctuations produce curvature, even if the expectation of the vacuum energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature.Comment: Accepted in Astrophysics and Space Scienc

Inflation with a constant ratio of scalar and tensor perturbation amplitudes

The single scalar field inflationary models that lead to scalar and tensor perturbation spectra with amplitudes varying in direct proportion to one another are reconstructed by solving the Stewart-Lyth inverse problem to next-to-leading order in the slow-roll approximation. The potentials asymptote at high energies to an exponential form, corresponding to power law inflation, but diverge from this model at low energies, indicating that power law inflation is a repellor in this case. This feature implies that a fine-tuning of initial conditions is required if such models are to reproduce the observations. The required initial conditions might be set through the eternal inflation mechanism. If this is the case, it will imply that the spectral indices must be nearly constant, making the underlying model observationally indistinguishable from power law inflation.Comment: 20 pages, 7 figures. Major changes to the Introduction following referee's comments. One figure added. Some other minor changes. No conclusion was modifie

Scalar field exact solutions for non-flat FLRW cosmology: A technique from non-linear Schr\"odinger-type formulation

We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schr\"{o}dinger (NLS)-type formulation in comparison to the method in the standard Friedmann framework. We consider phantom and non-phantom scalar field cases with exponential and power-law accelerating expansion. Analysis on effective equation of state to both cases of expansion is also performed. We speculate and comment on some advantage and disadvantage of using the NLS formulation in solving for the exact solution.Comment: 12 pages, GERG format, Reference added. accepted by Gen. Relativ. and Gra

Scalar field in cosmology: Potential for isotropization and inflation

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.Comment: 10 page

Regular black holes and black universes

We give a comparative description of different types of regular static, spherically symmetric black holes (BHs) and discuss in more detail their particular type, which we suggest to call black universes. The latter have a Schwarzschild-like causal structure, but inside the horizon there is an expanding Kantowski-Sachs universe and a de Sitter infinity instead of a singularity. Thus a hypothetic BH explorer gets a chance to survive. Solutions of this kind are naturally obtained if one considers static, spherically symmetric distributions of various (but not all) kinds of phantom matter whose existence is favoured by cosmological observations. It also looks possible that our Universe has originated from phantom-dominated collapse in another universe and underwent isotropization after crossing the horizon. An explicit example of a black-universe solution with positive Schwarzschild mass is discussed.Comment: 13 pages, 1 figure. 6 referenses and some discussion added, misprints correcte

Energy Conditions in f(G)f(G) Modified Gravity with Non-minimal Coupling to Matter

In this paper we study a model of modified gravity with non-minimal coupling between a general function of the Gauss-Bonnet invariant, $f(G)$, and matter Lagrangian from the point of view of the energy conditions. Such model has been introduced in Ref. [21] for description of early inflation and late-time cosmic acceleration. We present the suitable energy conditions for the above mentioned model and then, we use the estimated values of the Hubble, deceleration and jerk parameters to apply the obtained energy conditions to the specific class of modified Gauss-Bonnet models.Comment: 12 pages, no figur, Accepted for publication in Astrophysics and Space Scienc