Saddle point inflation from $f(R)$ theory

TL;DR

This paper explores saddle point inflation scenarios within power-law $f(R)$ gravity models, analyzing their stability and compatibility with PLANCK data, and finds that viable solutions resemble the Starobinsky model.

Contribution

It introduces specific $f(R)$ models with saddle points that produce stable inflationary solutions consistent with observational constraints.

Findings

Models can produce stable, PLANCK-compatible inflationary solutions.

Correct solutions typically start on the potential plateau, away from the saddle point.

Resemblance to the Starobinsky model in viable cases.

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.