Casimir Effect and Vacuum Energy

Abstract This chapter opens the part of the book devoted to quantum vacuum in non-trivial gravitational background and to vacuum energy. There are several macroscopic phenomena, which can be directly related to the properties of the physical quantum vacuum. The Casimir effect is probably the most accessible effect of the quantum vacuum. The chapter discusses different types of Casimir effect in condensed matter in restricted geometry, including the mesoscopic Casimir effect and the dynamic Casimir effect resulting in the force acting on a moving interface between 3He-A and 3He-B, which serves as a perfect mirror for the ‘relativistic’ quasiparticles living in 3He-A. It also discusses the vacuum energy and the problem of cosmological constant. Giving the example of quantum liquids it is demonstrated that the perfect vacuum in equilibrium has zero energy, while the nonzero vacuum energy arises due to perturbation of the vacuum state by matter, by texture, which plays the role of curvature, by boundaries due to the Casimir effect, and by other factors. The magnitude of the cosmological constant is small, because the present universe is old and the quantum vacuum is very close to equilibrium. The chapter discusses why our universe is flat, why the energies of the true vacuum and false vacuum are both zero, and why the perfect vacuum (true or false) is not gravitating.