Kinetic dominance and the wavefunction of the universe

Abstract

We analyze the emergence of classical inflationary universes in a kinetic-dominated stage using a suitable class of solutions of the Wheeler-De Witt equation with a constant potential. These solutions are eigenfunctions of the inflaton momentum operator that are strongly peaked on classical solutions exhibiting either or both a kinetic dominated period and an inflation period. Our analysis is based on semiclassical WKB solutions of the Wheeler-De Witt equation interpreted in the sense of Borel (to perform a correct connection between classically allowed regions) and on the relationship of these solutions to the solutions of the classical model. For large values of the scale factor the WKB Vilenkin tunneling wavefunction and the Hartle-Hawking no-boundary wavefunctions are recovered as particular instances of our class of wavefunctions.