Tunneling from nothing toward induced gravity inflation.

Abstract

We tackle the problem of the nucleation of the universe for the case in which the underlying gravity is an induced gravity with a Ginzburg-Landau potential for the scalar field. In order to make use of Vilenkin's wave function [Phys. Rev. D 33, 3560 (1986)], we cast the theory into its canonical Einstein form through a suitable conformal transformation: by using Vilenkin's boundary conditions we show then that the semiclassical tunneling from nothing solves the problem of the initial conditions in the induced gravity inflation and then selects the present observed values of the gravitational and the cosmological constants (${G}_{\mathrm{eff}}={G}_{N}$, ${\ensuremath{\Lambda}}_{\mathrm{eff}}=0$). Therefore our result is an improvement with respect to those obtained by other authors either (i) with the assumption of no-boundary conditions for the cosmic wave function, or (ii) with the same Ginzburg-Landau potential, but in the standard Einstein gravity.