Singular Instantons in Eddington-inspired-Born-Infeld Gravity

TL;DR

This paper explores instantons in EiBI gravity, revealing that some singularities can be regularized, but the auxiliary metric's singularity and quantum issues challenge their physical relevance.

Contribution

It provides a detailed analysis of instantons in EiBI gravity, showing how certain singularities are regularized and examining their implications for quantum stability.

Findings

Hawking-Moss instanton tunneling rate matches GR value

Singularities can be regularized in physical metrics but not in auxiliary metrics

Vilenkin instanton causes Minkowski instability, similar to GR

Abstract

In this work, we investigate $O(4)$-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI). We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.