A Singularity Problem with f(R) Dark Energy

TL;DR

There is a curvature singularity problem appearing on the nonlinear level that generally plagues f(R) models that modify Einstein gravity in the infrared, and the viability of many f( R) models in the current literature will have to be reevaluated.

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.

Figures (2)

• Figure 1: Effective potential of a scalar degree of freedom in $f(R)$ gravity model (\ref{['eq:star']}) with $\lambda=2$ and $n=1$. Diamonds mark the location of critical points. The part relevant to cosmological evolution is emphasized by thick blue line.
• Figure 2: Adding matter destabilizes the vacuum. Although effective potential inside constant density matter distribution still has a minimum, it is very shallow, and cannot protect the field $\phi$ from reaching curvature singularity $X$, which becomes energetically accessible from asymptotic vacuum state $B$.