Zeta-function approach to Casimir energy with singular potentials

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.Comment: 17 pages, 2 figures, added reference, address correcte

Gravitational particle production in braneworld cosmology

Gravitational particle production in time variable metric of an expanding universe is efficient only when the Hubble parameter $H$ is not too small in comparison with the particle mass. In standard cosmology, the huge value of the Planck mass $M_{Pl}$ makes the mechanism phenomenologically irrelevant. On the other hand, in braneworld cosmology the expansion rate of the early universe can be much faster and many weakly interacting particles can be abundantly created. Cosmological implications are discussed.Comment: 4 pages, 1 figure, v3 with new definition of $\Lambda$ and minor text modification

Short wavelength quantum electrodynamical correction to cold plasma-wave propagation

The effect of short wavelength quantum electrodynamic (QED) correction on plasma-wave propagation is investigated. The effect on plasma oscillations and on electromagnetic waves in an unmagnetized as well as a magnetized plasma is investigated. The effects of the short wavelength QED corrections are most significant for plasma oscillations and for extraordinary modes. In particular, the QED correction allow plasma oscillations to propagate, and the extra-ordinary mode looses its stop band. The significance of our results is discussed.Comment: 12 pages, 5 figure

Thermodynamics via Creation from Nothing: Limiting the Cosmological Constant Landscape

The creation of a quantum Universe is described by a {\em density matrix} which yields an ensemble of universes with the cosmological constant limited to a bounded range $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain $\Lambda<\Lambda_{\rm min}$ is ruled out by a cosmological bootstrap requirement (the self-consistent back reaction of hot matter). The upper cutoff results from the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost-avoidance renormalization. The cutoff $\Lambda_{\rm max}$ establishes a new quantum scale -- the accumulation point of an infinite sequence of garland-type instantons. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.Comment: RevTex, 4 pages, 4 figure

Attractive Casimir Forces in a Closed Geometry

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.Comment: An updated version to coincide with the one published December 2005 in PRL. 4 pages, 2 figure

Particle creation in a toroidal universe

We calculate the particle production rate in an expanding universe with a three-torus topology. We discuss also the complete evolution of the size of such a universe. The energy density of particles created through the nonzero modes is computed for selected masses. The unique contribution of the zero mode and its properties are also analyzed.Comment: 9 pages, 11 figure

Axion braneworld cosmology

We study axion cosmology in a 5D Universe, in the case of flat and warped extra dimension. The comparison between theoretical predictions and observations constrains the 5D axion decay constant and the 5D Planck mass, which has to be taken into account in building 5D axion models. The framework developed in this paper can be readily applied to other bulk fields in brane universes.Comment: uses revtex

Casimir force on a piston

We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L x b rectangular box, divided by a movable partition (piston) into two compartments of dimensions a x b and (L-a) x b. We compute the Casimir force on the piston in the limit L -> infinity. Regardless of the value of a/b, the piston is attracted to the nearest end of the box. Asymptotic expressions for the Casimir force on the piston are derived for a << b and a >> b.Comment: 10 pages, 1 figure. Final version, accepted for publication in Phys. Rev.

Casimir interaction of two plates inside a cylinder

The new exact formulas for the attractive Casimir force acting on each of the two identical perfectly conducting plates moving freely inside an infinite perfectly conducting cylinder with the same cross section are derived at zero and finite temperatures by making use of the zeta function technique. The long and short distance behaviour of the plates' free energy is investigated.Comment: 14 pages, 1 figure, latex2