Kinetic dominance and the wavefunction of the universe

TL;DR

This paper investigates how classical inflationary universes can emerge from a quantum cosmological framework, focusing on kinetic-dominated stages and analyzing solutions to the Wheeler-De Witt equation with implications for different wavefunction proposals.

Contribution

It introduces a class of solutions to the Wheeler-De Witt equation that are peaked on classical inflationary and kinetic-dominated solutions, connecting quantum wavefunctions with classical cosmology.

Findings

WKB solutions connect quantum and classical regimes.

Recovered Vilenkin tunneling and Hartle-Hawking wavefunctions as special cases.

Demonstrated emergence of classical inflationary universes from quantum states.

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.