Curvature Singularity in f(R) Theories of Gravity

TL;DR

This paper investigates the challenges of curvature singularities in f(R) gravity models, demonstrating that nonlinear evolution can lead to singularities, thus questioning the viability of these theories for explaining cosmic acceleration.

Contribution

It identifies and analyzes the emergence of curvature singularities in f(R) gravity models during scalar field evolution, highlighting a critical issue for their viability.

Findings

Curvature singularities can form during scalar field evolution in f(R) models.

Singularities occur near potential minima, affecting model viability.

Nonlinear dynamics in dust collapse can lead to unphysical divergences.

Abstract

Although $f(R)$ modification of late time cosmology is successful in explaining present cosmic acceleration, it is difficult to satisfy the fifth-force constraint simultaneously. Even when the fifth-force constraint is satisfied, the effective scalar degree of freedom may move to a point (close to its potential minima) in the field space where the Ricci scalar diverges. We elucidate this point further with a specific example of $f(R)$ gravity that incorporates several viable $f(R)$ gravity models in the literature. In particular, we show that the nonlinear evolution of the scalar field in pressureless contracting dust can easily lead to the curvature singularity, making this theory unviable.