Cosmic attractors and gauge hierarchy

We suggest a new cosmological scenario which naturally guarantees the smallness of scalar masses and vacuum expectation values, without invoking supersymmetry or any other (nongravitationally coupled) new physics at low energies. In our framework, the scalar masses undergo discrete jumps due to nucleation of closed branes during (eternal) inflation. The crucial point is that the step size of variation decreases in the direction of decreasing scalar mass. This scenario yields exponentially large domains with a distribution of scalar masses, which is sharply peaked around a hierarchically small value of the mass. This value is the "attractor point" of the cosmological evolution.