Cosmological Constant Seesaw in Quantum Cosmology

TL;DR

This paper introduces a quantum cosmology model where a seesaw mechanism explains the small observed cosmological constant by coupling universes with different vacuum energies, inspired by string theory insights.

Contribution

It provides a concrete realization of the cosmological constant seesaw mechanism within quantum cosmology using the Wheeler DeWitt equation and universe coupling.

Findings

Derives a relation for the cosmological constant similar to the seesaw mechanism.

Connects the model to string/M-theory cosmologies.

Suggests possible extensions with exact wave functions from string models.

Abstract

Recently a phenomenological relationship for the observed cosmological constant has been discussed by Motl and Carroll in the context of treating the cosmological constant as a $2\times 2$ matrix but no specific realization of the idea was provided. We realize a cosmological constant seesaw mechanism in the context of quantum cosmology. The main observation used is that a positive cosmological constant plays the role of a $Mass^2$ term in the Wheeler DeWitt (WDW) equation. Modifying the WDW equation to include a coupling between two universes, one of which has planck scale vacuum energy and another which has vacuum energy at the supersymmetry breaking scale before mixing, we obtain the relation $\lambda = (10TeV)^8/M_{Pl}^4$ in a similar manner to the usual seesaw mechanism. We discuss how the picture fits in with our current understanding of string/M-theory cosmologies. In particular we discuss how these results might be extended in the context of exact wave functions of the universe derived from certain string models.