The Gravitational Instability of the Vacuum: Insight into the Cosmological Constant Problem

A mechanism for suppressing the cosmological constant is developed, based on an analogy with a superconducting phaseshift in which free fermions coupled perturbatively to a weak gravitational field are in an unstable false vacuum state. The coupling of the fermions to the gravitational field generates fermion condensates with zero momentum and a phase transition induces a nonperturbative transition to a true vacuum state by producing a positive energy gap ∆ in the vacuum energy, identified with √ Λ, where Λ is the cosmological constant. In the strong coupling limit a large cosmological constant induces a period of inflation in the early universe, followed by a weak coupling limit in which √ Λ vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the density of Fermi surface fermions, D(ǫ), predicting a small cosmological constant in the present universe. emails: [email protected], [email protected], [email protected]