Semiclassical gravity with a nonminimally coupled scalar field

TL;DR

This paper explores semiclassical gravity with a nonminimally coupled scalar field, deriving the Wheeler-DeWitt equation, and finds wormhole solutions for various coupling constants, including the conformal case.

Contribution

It extends semiclassical gravity analysis to include nonminimal scalar coupling, revealing wormhole solutions even for large negative coupling constants.

Findings

Wave-functional admits wormhole boundary conditions for large negative epsilon.

Hawking-Page wormhole solution is recovered at conformal coupling epsilon=1/6.

Semiclassical approximation yields Einstein's equations and a Schrödinger equation for matter.

Abstract

Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a minimally coupled scalar field has been performed. To the leading order, vacuum Einstein's equation along with the functional Schrodinger equation for the matter field, propagating in the background of classical curved space are obtained. The Schrodinger equation is solved for a quartic potential. It is observed that the wave-functional admits the wormhole boundary condition even for large negative values of the coupling constant epsilon. For conformal coupling epsilon = 1/6, the Hawking-Page wormhole solution is recovered.