  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.
