Hidden Variables of Gravity and Geometry and the Cosmological Constant Problem

Abstract

We extend General Relativity by promoting Planck scale and the cosmological constant into integration constants, interpreted as fluxes of $4$-forms hiding in the theory. When we include the charges of the $4$-forms, these `constants' can vary discretely from region to region. We explain how the cosmological constant problem can be solved in this new framework. When the cosmological constant picks up contributions from two different $4$-forms, with an irrational ratio of charges, the spectrum of its values is a very fine discretuum. When the charges are mutually irrational, $\frac{2\kappa_{\tt eff}^2 \kappa^2 |{\cal Q}_i|}{3{\cal T}^2_i} < 1$, the discharge processes populating our discretuum will dynamically relax $\Lambda$, ceasing as $\Lambda$ approaches zero. Thus the theory exponentially favors a huge hierarchy $\Lambda/\mpl^4 \ll 1$ instead of $\Lambda/\mpl^4 \simeq 1$.