Abstract
Inflation with tunneling from a false to a true vacuum becomes viable in the presence of a scalar field that slows down the initial de Sitter phase. As a by-product this field also sets dynamically the value of ${M}_{\mathrm{Planck}}$ observed today. This can be very large if the tunneling rate (which is exponentially sensitive to the barrier) is small enough. Therefore along with inflation we also provide a natural dynamical explanation for why gravity is so weak today. Moreover we predict a spectrum of gravity waves peaked at around 0.1 mHz, that will be detectable by the planned space interferometer LISA. Finally we discuss interesting predictions on cosmological scalar and tensor fluctuations in light of the WMAP 3-year data.
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