Phantom Origin for f(R) Inflation

TL;DR

This paper explores how certain $f(R)$ gravity models can naturally lead to phantom-like inflationary behavior near de Sitter points, suggesting a possible pre-inflationary phantom phase and cyclic universe scenarios.

Contribution

It demonstrates that $f(R)=R+ ext{constant} imes R^n$ models with $1<n extless 3$ can exhibit phantom trajectories near de Sitter points, providing new insights into early universe dynamics.

Findings

Phantom trajectories tend to pass near de Sitter saddle points.

For $n=2$ and $n=3$, the models show special behavior with potential cosmological implications.

Numerical analysis supports the analytical dynamical system approach.

Abstract

We argue that for $f(R)=R+\alpha R^n$ model of the early universe, the de Sitter point appears as partial attractor for phantom paths. The phantom trajectories then bend their way to the oscillatory period passing near the de Sitter saddle point. Surprisingly, this vicinity is minimized for $1<n\le 3$ where a trajectory could cross the phantom border tangential to the de Sitter point. The only integers in this interval are $2$ and $3$ where $n=2$ reproduces also the most acceptable $f(R)$ model of inflation with strong motivations from quantum theory and also avoiding the vacuum meta-stability. Therefore, one may ask about a possible phantom pre-inflationary scenario. Combining with the increasing chance of falling in a phantom era in our time, proposing a singularity-free cyclic universe seems appealing, too. We use the dynamical system approach throughout this work which allows us to provide numerical support for the analytical discussions.