A Singularity Problem with f(R) Dark Energy

TL;DR

This paper identifies a curvature singularity issue in non-linear f(R) gravity models that challenges their viability, highlighting a problem invisible in linear analysis but critical for model stability.

Contribution

The paper reveals a fundamental curvature singularity problem in f(R) models at the non-linear level, impacting their physical viability.

Findings

Curvature singularity occurs at finite field values in f(R) models.

Linear analysis does not reveal the singularity, only oscillatory modes.

Many existing f(R) models may be invalidated due to this singularity issue.

Abstract

In this paper, I point out that there is a curvature singularity problem appearing on non-linear level that generally plagues f(R) models that modify Einstein gravity in the infrared. It is caused by the fact that for the effective scalar degree of freedom, the curvature singularity is at a finite field value and energy level, and can be easily accessed by the field dynamics in the presence of matter. This problem is invisible in linearized analysis, except for the tell-tale growing oscillatory modes it causes. In view of this, viability of many f(R) models in current literature will have to be re-evaluated.