Limits on the validity of the semiclassical theory

TL;DR

This paper investigates the limits of semiclassical gravity by examining energy-momentum fluctuations in a toy model, proposing a new criterion for validity, and concluding semiclassical theory is reliable only in coherent-like quantum states.

Contribution

It introduces a new criterion for the validity of semiclassical gravity and tests it using a toy model mimicking scalar field behavior in a Friedmann universe.

Findings

Semiclassical theory is reliable only in coherent-like states.

The new criterion outperforms previous ones in assessing validity.

Reliability depends on the quantum state's nature during evolution.

Abstract

For want of a more natural proposal, it is generally assumed that the back-reaction of a quantised matter field on a classical metric is given by the expectation value of its energy-momentum tensor, evaluated in a specified state. This proposal can be expected to be quite sound only when the fluctuations in the energy-momentum tensor of the quantum field are negligible. Based on this condition, a dimensionless criterion has been suggested earlier by Kuo and Ford for drawing the limits on the validity of this semiclassical theory. In this paper, we examine this criterion for the case of a toy model, constructed with two degrees of freedom and a coupling between them that exactly mimics the behaviour of a scalar field in a Friedmann universe. To reproduce the semiclassical regime of the field theory, in the toy model, one of degrees of freedom is assumed to be classical and the other quantum mechanical. Also the backreaction is assumed to be given by the expectation values of the quantum operators involved in the equations of motion for the classical system. Motivated by the same physical reasoning as Kuo and Ford, we, here, suggest another criterion, one which will be shown to perform more reliably as we evaluate these criterions for different states of the quantum system in the toy model. Finally, from the results obtained we conclude that the semiclassical theory being considered for the toy model is reliable, during all stages of its evolution, only if the quantum system is specified to be in coherent like states. The implications of these investigations on field theory are discussed.