Cosmological Constant Seesaw in Quantum Cosmology

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 $λ= (10TeV)^8/M_{Pl}^4$ 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.