  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 the Newton constant
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 inteferometer LISA.
Finally we discuss interesting predictions on cosmological scalar and tensor
fluctuations in the light the WMAP 3-year data.
