Possible Relation between the Cosmological Constant and Standard Model Parameters

Abstract

We propose possible properties of quantum gravity in de Sitter space, and find that they relate the value of the cosmological constant to parameters of the Standard Model. In de Sitter space we suggest (i) that the most sharply defined observables are obtained by scattering objects from the horizon and back to the horizon and (ii) that black holes of discrete charge are well defined states in the theory. For a black hole of minimal discrete electric charge, we therefore demand that a scattering process involving the black hole and a probe can take place within a Hubble time before evaporating away, so that the state of a discretely charged black hole is well defined. By imposing that the black hole's charge is in principle detectable, which involves appreciably altering the state of a scattered electron, we derive a relation between the Hubble scale, or cosmological constant, and the electron's mass and charge and order one coefficients that describe our ignorance of the full microscopic theory. This gives the prediction $\Lambda \sim 10^{-123 \pm 2} M_{Pl}^4$, which includes the observed value of dark energy. We suggest possible ways to test this proposal.