Abstract
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 nonlinear 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 nonperturbative ``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.
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