Initial conditions for slow-roll inflation in a random Gaussian landscape

Abstract

In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, $P\sim 10^{-3}$.

24 pages, 13 figures; (v2) minor changes, an appendix explaining new features of tunneling added

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• Note on initial conditions for small-field inflation
• 4-volume cutoff measure of the multiverse
• The Distribution of Vacua in Random Landscape Potentials
• Slepian models for Gaussian Random Landscapes
• TwInflation
• Barnacles and Gravity