Surface Tension and the Cosmological Constant

Abstract

The astronomically observed value of the cosmological constant is small but non-zero. This raises two questions together known as the cosmological constant problem a) why is lambda so nearly zero? b) why is lambda not EXACTLY zero? Sorkin has proposed that b) can be naturally explained as a one by square root N fluctuation by invoking discreteness of spacetime at the Planck scale due to quantum gravity. In this paper we shed light on these questions by developing an analogy between the cosmological constant and the surface tension of membranes. The ``cosmological constant problem'' has a natural analogue in the membrane context: the vanishingly small surface tension of fluid membranes provides an example where question a) above arises and is answered. We go on to find a direct analogue of Sorkin's proposal for answering question b) in the membrane context, where the discreteness of spacetime translates into the molecular structure of matter. We propose analogue experiments to probe a small and fluctuating surface tension in fluid membranes. A counterpart of dimensional reduction a la Kaluza-Klein and large extra dimensions also appears in the physics of fluid membranes.