We analyze the details of soft inflationary models, which have two scalar fields: one is the standard inflaton, whose potential is exponentially coupled to the other field. Such models are derived from both fundamental theories, and in the conformal frame of generalized Einstein theories. In the latter case, a nonstandard exponential coupling to the inflaton kinetic term also may arise. We list and discuss the various theories which give soft inflation, and then consider the satisfaction of the inflationary constraints in general models. We then specialize to new and chaotic inflation potentials, with both standard and nonstandard kinetic terms. The density perturbations are reduced sufficiently so that new inflation works well, with the coupling constant near the values allowed by grand unified theories. For chaotic inflation with a massive inflaton, we find successful inflation without any fine-tuning of the coupling constant or initial data.
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