Measures for a Transdimensional Multiverse

Abstract

The multiverse/landscape paradigm that has emerged from eternal inflation and string theory, describes a large-scale multiverse populated by "pocket universes" which come in a huge variety of different types, including different dimensionalities. In order to make predictions in the multiverse, we need a probability measure. In $(3+1)d$ landscapes, the scale factor cutoff measure has been previously shown to have a number of attractive properties. Here we consider possible generalizations of this measure to a transdimensional multiverse. We find that a straightforward extension of scale factor cutoff to the transdimensional case gives a measure that strongly disfavors large amounts of slow-roll inflation and predicts low values for the density parameter $\Omega$, in conflict with observations. A suitable generalization, which retains all the good properties of the original measure, is the "volume factor" cutoff, which regularizes the infinite spacetime volume using cutoff surfaces of constant volume expansion factor.

30 pages, 1 figure Minor revisions, reference added

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Cited by in corpus (10)

• Exploring a string-like landscape
• Geometric origin of coincidences and hierarchies in the landscape
• Decay of flux vacua to nothing
• An anisotropic universe due to dimension-changing vacuum decay
• Bubbles from Nothing
• Agnesi Weighting for the Measure Problem of Cosmology
• Phenomenology of the CAH+ measure
• Gravity waves from cosmic bubble collisions
• Multiverse rate equation including bubble collisions
• Measures for a Multidimensional Multiverse