MG11 
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Scalar Casimir Effect with Non-Local Boundary Conditions

Non-local boundary conditions have been considered in theoretical high-energy physics with emphasis on one-loop quantum cosmology, one-loop conformal anomalies, Bose-Einstein condensation models and spectral branes. We have therefore studied the Wightman function, the vacuum expectation value of the field square and the energy-momentum tensor for a massive scalar field satisfying non-local boundary conditions on a single and two parallel plates. Interestingly, we find that suitable choices of the kernel in the non-local boundary conditions lead to forces acting on the plates that can be repulsive for intermediate distances.

QUANTUM COSMOLOGY FROM THREE DIFFERENT PERSPECTIVES

This review is devoted to three promising research lines in quantum cosmology and the physics of the early universe. The nonperturbative renormalization programme is making encouraging progress that we here assess from the point of view of cosmological applications: Hamiltonian and Lagrangian form of pure gravity with variable G and Lambda; power-law inflation for pure gravity; an accelerating universe without dark energy. In perturbative quantum cosmology, on the other hand, diff-invariant boundary conditions lead naturally to a singularity-free one-loop wave function of the universe. Last, but not least, in the braneworld picture one discovers the novel concept of cosmological wave function of the bulk spacetime. Its impact on quantum cosmology is still, to a large extent, unexplored.