Low Energy Effective Hamiltonian for a Periodic Array of Cosmological Branes : The Smectic Universe

Abstract

We investigate a simple model of a stack of four dimensional cosmological branes in a five dimensional flat bulk via the use of a derived low-energy effective Hamiltonian for a `radion'-like field associated with brane displacements and deformations. We also extend by analogy the theory of 3D smectic liquid crystals and multi-lamellar amphiphilic membranes, as are typically found in soft condensed matter systems, to the 5D case of many parallel brane universes. The underlying rotational invariance of such a system implies the absence of an explicit intra-brane cosmological constant term in the low-energy effective Hamiltonian. The strength of a quadratic inter-brane potential introduced for stabilisation is calculated self-consistently, and leads naturally to a novel exponential suppression mechanism for the 4D intra-brane cosmological constant. We also pursue, again by analogy to the 3D case, the link between this work and the Abelian Higgs transition, or superconductivity, in 5D. The relevance of the work presented here in explicating the cosmological constant problem is also highlighted, outlined and discussed.