Casimir densities for a spherical boundary in de Sitter spacetime

Two-point functions, mean-squared fluctuations, and the vacuum expectation value of the energy-momentum tensor operator are investigated for a massive scalar field with an arbitrary curvature coupling parameter, subject to a spherical boundary in the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the sphere. Both the interior and exterior regions are considered. For the calculation in the interior region, a mode-summation method is employed, supplemented with a variant of the generalized Abel-Plana formula. This allows us to explicitly extract the contributions to the expectation values which come from de Sitter spacetime without boundaries. We show that the vacuum energy-momentum tensor is non-diagonal with the off-diagonal component corresponding to the energy flux along the radial direction. With dependence on the boundary condition and the mass of the field, this flux can be either positive or negative. Several limiting cases of interest are then studied. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively, far from the sphere. The decay of the boundary induced expectation values at large distances from the sphere is shown to be power-law (monotonic or oscillating), independent of the value of the field mass.Comment: 32 pages, 4 figures, new paragraph about generalizations, discussion and references added, accepted for publication in Phys. Rev.

Structure of Vector Mesons in Holographic Model with Linear Confinement

Wave functions and form factors of vector mesons are investigated in the holographic dual model of QCD with a smooth oscillator-like wall. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state (rho-meson), we show that, in this model, the basic elastic form factor exhibits the perfect vector meson dominance, i.e., it is given by the rho-pole contribution alone. The electric radius of the rho-meson is calculated, _C = 0.655 fm^2, which is larger than in case of the hard-wall cutoff. The squared radii of higher excited states are found to increase logarithmically rather than linearly with the radial excitation number. We calculate the coupling constant f_rho and find that the experimental value is closer to that calculated in the hard-wall model.Comment: 8 pages, RevTex4, references, comments and a figure added. Some terminoloy change