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We embed general $f(R)$ inflationary models in minimal supergravity plusmatter, a single chiral superfield $\Phi$, with or without another superfield$S$, via a Jordan frame Einstein+scalar description. In particular,inflationary models like a generalized Starobinsky one are analyzed andconstraints on them are found. We also embed the related models of conformalinflation, also described as Jordan frame Einstein+scalar models, in particularthe conformal inflation from the Higgs model, and analyze the inflationaryconstraints on them.

General $f(R)$ and conformal inflation from minimal supergravity plus matter