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We consider a wide class of four-dimensional effective field theories inwhich gravity is coupled to multiple four-forms and their dual scalar fields,with membrane sources charged under the corresponding three-form potentials.Four-form flux, quantised in units of the membrane charges, genericallygenerates a landscape of vacua with a range of values for the cosmologicalconstant that is scanned through membrane nucleation. We list various ways inwhich the landscape can be made sufficiently dense to be compatible withobservations of the current vacuum without running into the empty universeproblem. Further, we establish the general criteria required to ensure theabsolute stability of the Minkowski vacuum under membrane nucleation and thelongevity of those vacua that are parametrically close by. This selects thecurrent vacuum on probabilistic grounds and can even be applied in the classicmodel of Bousso and Polchinski, albeit with some mild violation of the membraneweak gravity conjecture. We present other models where the membrane weakgravity conjecture is not violated but where the same probabilistic methods canbe used to tackle the cosmological constant problem.

The cosmological constant is probably still zero