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 to gravitons are in an unstable false vauum. 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 $\mathrm{\Delta }$ in the vacuum energy identified with $\sqrt{\mathrm{\Lambda }}$, where $\mathrm{\Lambda }$ 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 $\sqrt{\mathrm{\Lambda }}$ vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the Fermi surface fermions, predicting a small cosmological constant in the early universe.