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

Stephon Alexander·Manasse Mbonye·John Moffat
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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 $Δ$ in the vacuum energy, identified with $\sqrtΛ$, 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 $\sqrtΛ$ vanishes exponentially fast as the universe expands due to the dependence of the energy gap on the density of Fermi surface fermions, $D(ε)$, predicting a small cosmological constant in the present universe.

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Stephon Alexander, Manasse Mbonye, John Moffat. 2004-06-23. The Gravitational Instability of the Vacuum: Insight into the Cosmological Constant Problem. https://arxiv.org/abs/hep-th/0406202

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