### 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).