Gravitational Instability of the Vacuum and the Cosmological Constant Problem

TL;DR

This paper proposes a mechanism using a superconducting analogy to explain how the universe's vacuum energy can be suppressed, leading to a small cosmological constant consistent with observations.

Contribution

It introduces a non-perturbative phase transition model where fermion condensates reduce the cosmological constant over cosmic time.

Findings

Large initial cosmological constant causes early universe inflation.

Fermion condensates generate a positive energy gap related to the cosmological constant.

The energy gap decreases exponentially, explaining the small present-day cosmological constant.

Abstract

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 $\Delta$ 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 Fermi surface fermions, predicting a small cosmological constant in the early universe.