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The conditions on the effective (de Sitter space) scalar potential that are required to obtain a successful new-inflationary-Universe scenario are codified into a general prescription. These conditions ensure that sufficient inflation, density fluctuations of an acceptable magnitude, and reheating to a high enough temperature to produce the astrophysically observed baryon asymmetry result. We exemplify our prescription for a quartic potential and show that if the scalar field is a gauge singlet, then it is possible to tune the parameters of the potential to satisfy the conditions we have prescribed.
Steinhardt et al. (Tue,) studied this question.