Gravitational instability of the vacuum and the cosmological constant problem

A mechanism for suppressing the cosmological constant is described, using a superconducting analogy in which fermions coupled perturbatively to gravitons are in an unstable false vacuum. The coupling of the fermions to gravitons and a screened attractive interaction among pairs of fermions generates fermion condensates with zero momentum and a phase transition induces a non-perturbative transition to a true vacuum state. This produces a positive energy gap A in the vacuum energy identified with VIA, where A 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 root Lambda vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the density of Fermi surface fermions, predicting a small cosmological constant in the early universe.