Saddle point inflation from $f(R)$ theory

Abstract

We analyse several saddle point inflationary scenarios based on power-law $f(R)$ models. We investigate inflation resulting from $f(R)=R+{\alpha }_n{M}^{2(1-n)}{R}^n+{\alpha }_{n+1}{M}^{-2n}{R}^{n+1}$ and $f(R)={\sum }_n^l{\alpha }_n{M}^{2(1-n)}{R}^n$ as well as $l\to \infty$ limit of the latter. In all cases we have found relation between ${\alpha }_n$ coefficients and checked consistency with the PLANCK data as well as constraints coming from the stability of the models in question. Each of the models provides solutions which are both stable and consistent with PLANCK data, however only in parts of the parameter space where inflation starts on the plateau of the potential, some distance from the saddle. And thus all the correct solutions bear some resemblance to the Starobinsky model.

10 pages, 8 figures

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Cited by in corpus (5)

• Precision Predictions for the Primordial Power Spectra from f(R) Models of Inflation
• Endlessly flat scalar potentials and $\alpha$-attractors
• Saddle point inflation from higher order corrections to Higgs/Starobinsky inflation
• Multi-phase induced inflation in theories with non-minimal coupling to gravity
• Implications of extreme flatness in a general f(R) theory