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 ΩB/ΩDM. Here we consider generation of domains of different baryon density via random variations of the phase or magnitude of a complex field Φ during inflation. Baryon isocurvature perturbations are a natural consequence of any such mechanism. We derive baryon isocurvature bounds on the expansion rate during inflation HI and on the mass parameter μ which breaks the global U(1) symmetry of the Φ potential. We show that when μ ∼< HI (as expected in SUSY models) the baryon isocurvature constraints can be satisfied only if HI is unusually small, HI < 107GeV, or if non-renormalizable Planck-suppressed corrections to the Φ potential are excluded to a high order. Alternatively, an unsuppressed Φ potential is possible if μ is sufficiently large, μ ∼> 1016GeV. 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