Quantum Mechanical Lorentzian Wormholes in Cosmological Backgrounds

TL;DR

This paper analyzes quantum Lorentzian wormholes within cosmological backgrounds using the Wheeler-DeWitt equation, revealing their dynamic behavior and size evolution in radiation and deSitter universes.

Contribution

It provides a minisuperspace quantum analysis of Lorentzian wormholes in cosmological backgrounds, deriving their wavefunctions and size evolution.

Findings

Wormhole throat radius relaxes to Planck scale in radiation backgrounds.

In deSitter backgrounds, the radius remains stationary and above Planck length.

Quantum effects influence wormhole size dynamics in early universe scenarios.

Abstract

We present a minisuperspace analysis of a class of Lorentzian wormholes that evolves quantum mechanically in a background Friedman Robertson Walker spacetime. The quantum mechanical wavefunction for these wormholes is obtained by solving the Wheeler-DeWitt equation for Einstein gravity on this minisuperspace. The time-dependent expectation value of the wormhole throat radius is calculated to lowest order in an adiabatic expansion of the Wheeler-DeWitt hamiltonian. For a radiation dominated expansion, the radius is shown to relax asymptotically to obtain a value of order the Planck length while for a deSitter background, the radius is stationary but always larger than the Planck length. These two cases are of particular relevance when considering wormholes in the early universe.