Casimir energy and brane stability

Abstract

We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S 1 /Z Z 2 orbifold, which includes the Randall-Sundrum two brane model (RS1). We employ a ζ-function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produce a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of the fine-tuning needed for stabilization of the brane spearation. Lastly, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.

Kaluza-Klein models as pistons

“…The scalar Casimir force between parallel plates in the presence of compactified extra dimensions has been used to put restrictions on the size of the extra dimensions [6,7,20,21,31,44]; for more recent discussions of perfectly conducting parallel plates affecting the five-component electromagnetic field in five dimensions (reaching different conclusions) see [13,45]. The Casimir effect was also used to argue against the possibility that vacuum energy plays the role of a cosmological constant responsible for the observed dark energy [8,41,46]; cutoff scales that could produce the needed dark energy led to the prediction of repulsive Casimir forces at distances between the plates where attraction is verified experimentally [3,36,43].…”

Æther field, Casimir energy and stabilization of the extra dimension

“…The effects of the aether fields on cosmological observable was studied in [10]. The authors in [11,12] also studied the role of aether field on the stability of the extra dimension in the context of braneword scenario but in a different aspect.…”

Casimir energy and topological mass for a massive scalar field with Lorentz violation

“…In these contexts, Casimir energy has been considered in Refs. [20,21] and [22][23][24], respectively. Therefore, with such a great number of theoretical works, it is natural that the search for Lorentz symmetry violations also acquire experimental interest and, in this sense, the Casimir effect becomes an even more interesting topic to study, since it can be related with Lorentz symmetry violation models.…”