Some quantum effects in cosmological models

We will investigate the combined effects of background curvature and boundaries on the properties of quantum vacuum for scalar and fermionic fields. As background geometries, de Sitter (dS) and anti-de Sitter (AdS) spacetimes will be considered. The dS spacetime is described in coordinates with negative curvature spatial foliation. As a boundary a spherical shell will be taken on which the scalar field obeys the Robin boundary condition and the fermionic field is constrained by the bag boundary condition. The vacuum expectation values of the field squared and of the energy-momentum tensor, as well as the Casimir forces will be investigated inside and outside the sphere. In the second class of problems the background geometry is described by locally AdS spacetime with a part of spatial dimensions compactified on a torus. The fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a charged fermionic field will be evaluated in the presence of branes parallel to the AdS horizon. The vacuum expectation values of the field squared, of the energy-momentum tensor and of the current density for a charged scalar field will be investigated in the geometry of a finite thickness brane, embedded in the AdS bulk with compact dimensions.