Superpotential method for $F(R)$ cosmological models

Abstract

We construct the $F(R)$ gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions $F(R)$ are obtained explicitly. We consider exact solutions for the obtained $R^2$ gravity model with the cosmological constant in detail.

arXiv comment10 pages, references added

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• Analytic extensions of Starobinsky model of inflation
• On the superstring-inspired quantum correction to the Starobinsky model of inflation
• Exact and slow-roll solutions for exponential power-law inflation connected with f(R) gravity and observational constraints
• Integrable modified gravity cosmological models with an additional scalar field
• Superpotential method and the amplification of inflationary perturbations
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• New one-parametric extension of the Starobinsky inflationary model
• New Integrable Chiral Cosmological Models with Two Scalar Fields
• Eisenhart-Duval lift, Nonlocal Conservation laws and Painlevé Analysis in Scalar field Cosmology
• Scheme of integration of vacuum $F(R)$ gravity in a travelling wave variable