Problem of Unitarity and Quantum Corrections in Semiclassical Quantum Gravity

TL;DR

This paper explores how to maintain unitarity in semiclassical quantum gravity using the de Broglie-Bohm interpretation, leading to a nonlinear gravitational equation and quantum corrections in a cosmological model.

Contribution

It introduces a novel representation of semiclassical quantum gravity that preserves unitarity through a nonlinear gravitational equation and develops a perturbation method for quantum corrections.

Findings

A nonlinear gravitational equation compatible with unitarity.

Quantum corrections to matter fields in a cosmological setting.

Semiclassical Einstein equation with quantum corrections for FRW model.

Abstract

Using both the Born-Oppenheimer idea and the de Broglie-Bohm interpretation of wavefunction we represent in a different way the semiclassical quantum gravity from the Wheeler-DeWitt equation in an oscillating regime which can preserve completely the unitary quantum evolution of a matter field at the expense of a nonlinear gravitational field equation, but has the same asymptotic limit as the others. We apply the de Broglie-Bohm interpretation to the nonlinear gravitational field equation to develop a perturbation method to find the quantum corrections of a matter field to the gravity. The semiclassical Einstein equation with the quantum corrections is found for a minimal quantum FRW cosmological model.