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

TL;DR

This paper proposes a mechanism where fermion condensates and phase transitions in a gravitational context can naturally suppress the cosmological constant, explaining its small observed value through early universe inflation and subsequent decay.

Contribution

It introduces a novel analogy between superconducting phase shifts and vacuum instability, providing a nonperturbative model for the cosmological constant problem.

Findings

Large initial cosmological constant causes early universe inflation.

The energy gap decreases exponentially, leading to a small present-day cosmological constant.

The model links fermion density to the suppression of the cosmological constant.

Abstract

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 $\Delta$ in the vacuum energy, identified with $\sqrt{\Lambda}$, where $\Lambda$ 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 $\sqrt{\Lambda}$ vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the density of Fermi surface fermions, $D({\epsilon})$, predicting a small cosmological constant in the present universe.