  We study a first-order formulation for the coupled evolution of a quantum
scalar field and a classical Friedmann universe. The model is defined by a
state dependent hamiltonian constraint and the time dependent Schr\"odinger
equation for the scalar field. We solve the resulting non-linear equations
numerically for initial data consisting of a Gaussian scalar field state and
gravity phase space variables. This gives a self-consistent semiclassical
evolution that includes non-perturbative ``backreaction" due to particle
production. We compare the results with the evolution of a quantum scalar field
on a fixed background, and find that the backreaction modifies both particle
production and cosmological expansion, and that these effects remain bounded.
