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

Casimir energy of a non-uniform string

The Casimir energy of a non-uniform string built up from two pieces with different speed of sound is calculated. A standard procedure of subtracting the energy of an infinite uniform string is applied, the subtraction being interpreted as the renormalization of the string tension. It is shown that in the case of a homogeneous string this method is completely equivalent to the zeta renormalization.Comment: 11 pages, REVTeX, no figures and table

Shear Viscosity of Yang-Mills Theory in the Confinement Phase

In terms of a simple holographic model, we study the absorption cross section and the shear viscosity of a pure Yang-Mills field at low temperature where the system is in the confinement phase. Then we expect that the glueball states are the dominant modes in this phase. In our holographic model an infrared cutoff r_m is introduced as a parameter which fixes the lowest mass of the glueball. As a result the critical temperature of gluon confinement T_c is estimated to be about 127 MeV. For T < T_c, we find that both the absorption cross section and the shear viscosity are independent of the temperature. Their values are frozen at the values corresponding to the critical point, for 0 < T < T_c. We discuss this behavior by considering the glueball mass and its temperature dependence.Comment: 11 pages latex, 2 figures; minor changes in the discussion, reference added. To appear in Int. J. Mod. Phys.

Casimir energy of a dilute dielectric ball in the mode summation method

In the $(\epsilon_1-\epsilon_2)^2$--approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a closed form the sum over the angular momentum before the integration over the imaginary frequencies. The linear in $(\epsilon_1-\epsilon_2)$ contribution into the vacuum energy is removed by an appropriate subtraction. The role of the contact terms used in other approaches to this problem is elucidated.Comment: 14 pages, REVTeX, no figures, no tables; presentation is made better, new references are adde

Casimir Surface Force on a Dilute Dielectric Ball

The Casimir surface force density F on a dielectric dilute spherical ball of radius a, surrounded by a vacuum, is calculated at zero temperature. We treat (n-1) (n being the refractive index) as a small parameter. The dispersive properties of the material are taken into account by adopting a simple dispersion relation, involving a sharp high frequency cutoff at omega = omega_0. For a nondispersive medium there appears (after regularization) a finite, physical, force F^{nondisp} which is repulsive. By means of a uniform asymptotic expansion of the Riccati-Bessel functions we calculate F^{nondisp} up to the fourth order in 1/nu. For a dispersive medium the main part of the force F^{disp} is also repulsive. The dominant term in F^{disp} is proportional to (n-1)^2{omega_0}^3/a, and will under usual physical conditions outweigh F^{nondisp} by several orders of magnitude.Comment: 24 pages, latex, no figures, some additions to the Acknowledments sectio

Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in previous version corrected, giving a zero Casimir energy for a tenuous cylinde

Casimir energy of a dilute dielectric ball with uniform velocity of light at finite temperature

The Casimir energy, free energy and Casimir force are evaluated, at arbitrary finite temperature, for a dilute dielectric ball with uniform velocity of light inside the ball and in the surrounding medium. In particular, we investigate the classical limit at high temperature. The Casimir force found is repulsive, as in previous calculations.Comment: 15 pages, 1 figur

Casimir energy and realistic model of dilute dielectric ball

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity $\epsilon(i\omega)$. A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance $\lambda$ is a {\it physical} cut-off in the theory. This fact has been overlooked before, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics.Comment: 12 pages, 1 figure, latex 2e, journal versio

Casimir attractive-repulsive transition in MEMS

Unwanted stiction in micro- and nanomechanical (NEMS/MEMS) systems due to dispersion (van der Waals, or Casimir) forces is a significant hurdle in the fabrication of systems with moving parts on these length scales. Introducing a suitably dielectric liquid in the interspace between bodies has previously been demonstrated to render dispersion forces repulsive, or even to switch sign as a function of separation. Making use of recently available permittivity data calculated by us we show that such a remarkable non-monotonic Casimir force, changing from attractive to repulsive as separation increases, can in fact be observed in systems where constituent materials are in standard NEMS/MEMS use requiring no special or exotic materials. No such nonmonotonic behaviour has been measured to date. We calculate the force between a silica sphere and a flat surface of either zinc oxide or hafnia, two materials which are among the most prominent for practical microelectrical and microoptical devices. Our results explicate the need for highly accurate permittivity functions of the materials involved for frequencies from optical to far-infrared frequencies. A careful analysis of the Casimir interaction is presented, and we show how the change in the sign of the interaction can be understood as a result of multiple crossings of the dielectric functions of the three media involved in a given set-up.Comment: 6 pages, 4 figure

Crossing of the w=-1 Barrier in Two-Fluid Viscous Modified Gravity

Singularities in the dark energy late universe are discussed, under the assumption that the Lagrangian contains the Einstein term R plus a modified gravity term of the form R^\alpha, where \alpha is a constant. It is found, similarly as in the case of pure Einstein gravity [I. Brevik and O. Gorbunova, Gen. Rel. Grav. 37 (2005), 2039], that the fluid can pass from the quintessence region (w>-1) into the phantom region (w<-1) as a consequence of a bulk viscosity varying with time. It becomes necessary now, however, to allow for a two-fluid model, since the viscosities for the two components vary differently with time. No scalar fields are needed for the description of the passage through the phantom barrier.Comment: 16 pages latex, no figure