Calculations of the Casimir Effect in Cosmology

Emilio Elizalde

Instituto de Ciencias del Espacio (ICE/CSIC)

Institut d'Estudis Espacials de Catalunya (IEEC/CSIC)

Departament ECM

Facultat de Física

Universitat de Barcelona

Edifici Nexus, Gran Capità, 2-4,

08034 Barcelona, Spain.

As is well known ---and most clearly explained in a recent paper by Björken--- a non-zero cosmological constant in Einstein's (or FRW) equations can be traded for the presence of a vacuum
energy density corresponding to some fundamental field, and may have an influence down to the level of particle physics. It is thus very interesting to calculate the Casimir effect in cosmological models, as is the case of braneworld universes. This will be done for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS branes, some of which may correspond to our universe. These computations of the Casimir effect in cosmology turn out to be rather non-trivial. They will be carried out using zeta-function regularization, which advantageously yields the different mass and/or temperature expansions for the effective potential. Using these results, some basic issues as the possibility of brane stabilization using the Casimir force only, or getting the observational value of the cosmological constant in the physical brane, can be discussed.

Work done in collaboration with Shin'ichi Nojiri (Kyoto), Sergei D. Odintsov (Tomsk), Sachiko Ogushi (Kyoto), and Alex Tort (Rio de Janeiro).