Superpotential method and the amplification of inflationary perturbations

Abstract

The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to drive inflation and lead to the amplification of the curvature perturbations. Such an amplification, at wavelengths shorter than those observed in the cosmic microwave background, is necessary in order to have a significant formation of primordial black holes after inflation ends. The technique is applied to the cases of a minimally coupled inflaton, to the nonminimal coupling case and to $f(R)$ theories of gravity. For such theories, a model dependent analysis of the features leading to the scalar spectrum enhancement is also presented.

17 pages, final version accepted for publication on PRD

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Cited by in corpus (7)

• Inflation in $F(R)$ gravity models revisited after ACT
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• More accurate slow-roll approximations for inflation in scalar-tensor theories
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• Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity