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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 < H_{I} (as expected in SUSY models) the baryon isocurvature constraints can be satisfied only if H_{I} is unusually small, H_{I} < 10^{7} GeV, or if non-renormalizable Planck-suppressed corrections to the Phi potential are excluded to a high order. Alternatively, an unsuppressed Phi potential is possible if mu is sufficiently large, mu > 10^{16} GeV. We show that the baryon isocurvature constraints can be naturally satisfied in Affleck-Dine baryogenesis, as a result of the high-order suppression of non-renormalizable terms along MSSM flat directions.