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.
