Cusp singularities in f(R) gravity: pros and cons

TL;DR

This paper explores cusp singularities in f(R) gravity models, demonstrating their formation during gravitational collapse through simulations, and discusses potential observational implications and ways to mitigate these singularities.

Contribution

It provides numerical evidence that cusp singularities can be triggered in f(R) gravity during collapse and examines how quadratic terms can cure them, highlighting observational challenges.

Findings

Cusp singularities can be formed during gravitational collapse in f(R) gravity.

Adding a quadratic term can cure cusp singularities but introduces observable Ricci scalar bumps.

Detecting super-Planckian effects in astrophysics remains challenging.

Abstract

We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvature singularity that can be interpreted by a firewall.