Scale of gravity and the cosmological constant within a landscape

It is possible that the scale of gravity, parametrized by the apparent Planck mass, may obtain different values within different universes in an encompassing multiverse. We investigate the range over which the Planck mass may scan while still satisfying anthropic constraints. The window for anthropically allowed values of the Planck mass may have important consequences for landscape predictions. For example, if the likelihood to observe some value of the Planck mass is weighted by the inflationary expansion factors of the universes that contain that value, then it appears extremely unlikely to observe the value of the Planck mass that is measured within our universe. This is another example of the runaway inflation problem discussed in recent literature. We also show that the window for the Planck mass significantly weakens the anthropic constraint on the cosmological constant when both are allowed to vary over a landscape.