Casimir Effect for the Piecewise Uniform String

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. In its simplest version the string consists of two parts I and II having in general different tension and mass density, but is always obeying the condition that the velocity of sound is equal to the velocity of light. The model, first introduced by Brevik and Nielsen in 1990, possesses attractive formal properties implying that it becomes easily regularizable by several methods, the most powerful one being the contour integration method. We also consider the case where the string is divided into 2N pieces, of alternating type-I and type-II material. The free energy at finite temperature, as well as the Hagedorn temperature, are found. Finally, we make some remarks on the relationship between this kind of theory and the theory of quantum star graphs, recently considered by Fulling et al.Comment: 10 pages, 1 figure, Submitted to the volume "Cosmology, Quantum Vacuum, and Zeta Functions", in honour of Professor Emilio Elizalde on the occasion of his 60th birthda

Viscous Cosmology and the Cardy-Verlinde Formula

The holographic principle in a radiation dominated universe is extended to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be possible from a formal point of view, although we question on physical grounds the manner in which the Casimir energy is evaluated in this case. Also, we consider an observation recently made by Youm, namely that the entropy of the universe is no longer expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance equation of state and instead merely assumes that the pressure is proportional to the energy density. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but endowed with a constant bulk viscosity.Comment: 10 pages, no figures. Contribution to the Proceedings of the Second Londrina Winter School "Mathematical Methods in Physics", August 25-30, 2002, Londrina-Parana, Brazi

Casimir Theory of the Relativistic Composite String Revisited, and a Formally Related Problem in Scalar QFT

The main part of this paper is to present an updated review of the Casimir energy at zero and finite temperature for the transverse oscillations of a piecewise uniform closed string. We make use of three different regularizations: the cutoff method, the complex contour integration method, and the zeta-function method. The string model is relativistic, in the sense that the velocity of sound is for each string piece set equal to the velocity of light. In this sense the theory is analogous to the electromagnetic theory in a dielectric medium in which the product of permittivity and permeability is equal to unity (an isorefractive medium). We demonstrate how the formalism works for a two-piece string, and for a 2N-piece string, and show how in the latter case a compact recursion relation serves to facilitate the formalism considerably. The Casimir energy turns out to be negative, and the more so the larger the number of pieces in the string. The two-piece string is quantized in D-dimensional spacetime, in the limit when the ratio between the two tensions is very small. We calculate the free energy and other thermodynamic quantities, demonstrate scaling properties, and comment on the meaning of the Hagedorn critical temperature for the two-piece string. Thereafter, as a novel development we present a scalar field theory for a real field in three-dimensional space in a potential rising linearly with a longitudinal coordinate z in the interval 0<z<1, and which is thereafter held constant on a horizontal plateau. The potential is taken as a rough model of the two-piece string potential under simplifying conditions, when the length ratio between the pieces is replaced formally with the mentioned length parameter z.Comment: 24 latex pages, one figure. Contribution to the honorary issue of J. Phys. A, on the occasion of the 75th anniversary of Professor Stuart Dowker. The present version, augmented by a section on a related one-dimensional problem in scalar QFT, matches the forthcoming published versio

Viscosity-Induced Crossing of the Phantom Divide in the Dark Cosmic Fluid

Choosing various natural forms for the equation-of-state parameter w and the bulk viscosity \zeta, we discuss how it is possible for a dark energy fluid to slide from the quintessence region across the divide w=-1 into the phantom region, and thus into a Big Rip future singularity. Different analytic forms for \zeta, as powers of the scalar expansion, are suggested and compared with experiments.Comment: 11 pages latex, no figure

Quantum Annihilation of Anti- de Sitter Universe

We discuss the role of conformal matter quantum effects (using large $N$ anomaly induced effective action) to creation-annihilation of an Anti-de Sitter Universe. The arbitrary GUT with conformally invariant content of fields is considered. On a purely gravitational (supersymmetric) AdS background, the quantum effects act against an (already existing) AdS Universe. The annihilation of such a Universe occurs, what is common for any conformal matter theory. On a dilaton-gravitational background, where there is dilatonic contribution to the induced effective action, the quantum creation of an AdS Universe is possible assuming fine-tuning of the dilaton.Comment: 7 pages, LaTeX, no figures, minor modifications. Version to appear in Phys. Lett.

Casimir Effects Near the Big Rip Singularity in Viscous Cosmology

Analytical properties of the scalar expansion in the cosmic fluid are investigated, especially near the future singularity, when the fluid possesses a constant bulk viscosity \zeta. In addition, we assume that there is a Casimir-induced term in the fluid's energy-momentum tensor, in such a way that the Casimir contributions to the energy density and pressure are both proportional to 1/a^4, 'a' being the scale factor. A series expansion is worked out for the scalar expansion under the condition that the Casimir influence is small. Close to the Big Rip singularity the Casimir term has however to fade away and we obtain the same singular behavior for the scalar expansion, the scale factor, and the energy density, as in the Casimir-free viscous case.Comment: 7 pages RevTeX, no figures. Minor changes in discussion, some references added. To appear in Gen. Rel. Gra