  A wide variety of vacua, and their cosmological realization, may provide an
explanation for the apparently anthropic choices of some parameters of particle
physics and cosmology. If the probability on various parameters is weighted by
volume, a flat potential for slow-roll inflation is also naturally understood,
since the flatter the potential the larger the volume of the sub-universe.
However, such inflationary landscapes have a serious problem, predicting an
environment that makes it exponentially hard for observers to exist and giving
an exponentially small probability for a moderate universe like ours. A general
solution to this problem is proposed, and is illustrated in the context of
inflaton decay and leptogenesis, leading to an upper bound on the reheating
temperature in our sub-universe. In a particular scenario of chaotic inflation
and non-thermal leptogenesis, predictions can be made for the size of CP
violating phases, the rate of neutrinoless double beta decay and, in the case
of theories with gauge-mediated weak scale supersymmetry, for the fundamental
scale of supersymmetry breaking.
