Anthropically selected baryon number and isocurvature constraints

The similarity of the observed baryon and dark matter densities suggests that they are physically related, either via a particle physics mechanism or anthropic selection. A pre-requisite for anthropic selection is the generation of superhorizon-sized domains of different Omega(B)/Omega(DM). Here we consider generation of domains of different baryon density via random variations of the phase or magnitude of a complex field Phi during inflation. Baryon isocurvature perturbations are a natural consequence of any such mechanism. We derive baryon isocurvature bounds on the expansion rate during inflation H-I and on the mass parameter mu which breaks the global U(1) symmetry of the Phi potential. We show that when mu less than or similar to H-I (as expected in SUSY models) the baryon isocurvature constraints can be satisfied only if H-I is unusually small, H-I