Abstract
We present the renormalized equations which rule the evolution of the mean value of the field and the metric of the spacetime for the lambdaphi/sup 4/ theory. The calculations are done in the one-loop approximation and the classical background gravitational field is a general one. For the particular example of a Robertson-Walker metric, we show that the numerical method used to solve the back-reaction problem in the free-field case can also be applied here without additional complications. We discuss the possible generalizations of our formalism and its relevance in the study of phase transitions in the early Universe.
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