Casimir effect in de Sitter and anti–de Sitter braneworlds

Abstract

We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS brane, which may correspond to our universe. Using zeta-regularization, the interesting conclusion is reached, that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.

The Casimir effect in the presence of compactified universal extra dimensions

“…• The question how vacuum fluctuations affect the * Electronic address: katjap@th.physik.uni-frankfurt.de stability of extra dimensions has been explored in [16,17,18,19,20,21]. Especially the detailed studies in the Randall-Sundrum model have shown the major contribution of the Casimir effect to stabilise the radion [22,23,24,25].…”

Zeta functions in brane world cosmology

“…[22,24] nor by that of Refs. [21,23]. In order to find some explanation for the difference, let us briefly reconsider the method used there.…”

“…The cases of a massless conformally coupled scalar field and of a massive minimally coupled field for de Sitter branes embedded in both de Sitter and AdS bulks have been considered in Ref. [23], where the vacuum energy is computed once again by using conformal and zeta regularization techniques and is found to be zero for the one brane case. Refs.…”

“…First we specify the result to the conformally coupled case and compare with that of Refs. [21,22,23,24]. Then we consider the limit of large AdS curvature radius ℓ, which should reproduce a ball-like geometry.…”

Qualitative study in loop quantum cosmology

“…We can mention, for instance, the assumption of a non-linear EoS [10] with two fixed points where the pressure plus energy density vanishes, or the modification of the Friedmann equation assuming that the square of the Hubble parameter is equal to a power series of the energy density [11]. Another option is the introduction of higher order terms in the equations of GR via the quantum effects of a scalar field conformally coupled with gravity [12][13][14][15][16] or directly assuming a Lagrangian containing non-linear terms in the scalar curvature [17][18][19]. However, the simplest way to remove the Big Bang singularity is to adopt the viewpoint of Loop Quantum Cosmology (LQC), where the discrete nature of spacetime is assumed and Friedmann equations are modified (see for review [20,21]).…”