Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

Folkert Kuipers,Xavier Calmet

doi:10.3390/universe6100171

Abstract

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

Highlights

The significance of singularity theorems in general relativity first presented in the seminal papers of Penrose and Hawking [1,2] cannot be overemphasised
We shall assume that the physics responsible for the avoidance of singularities becomes relevant at energies below the Planck scale and can be described within our mathematical framework; an example would be, e.g., a bounce solution in a stellar collapse to a black hole [19] or in Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology which would avoid a Big Crunch solution [20]
We note that this approach goes beyond general relativity and it is applicable to any theory of quantum gravity that does not break diffeomorphism invariance

Summary

Introduction

The significance of singularity theorems in general relativity first presented in the seminal papers of Penrose and Hawking [1,2] cannot be overemphasised. We discuss the validity of the singularity theorems in the framework of the effective field theory approach to quantum gravity. We shall assume that the physics responsible for the avoidance of singularities becomes relevant at energies below the Planck scale and can be described within our mathematical framework; an example would be, e.g., a bounce solution in a stellar collapse to a black hole [19] or in Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology which would avoid a Big Crunch solution [20] We note that this approach goes beyond general relativity and it is applicable to any theory of quantum gravity that does not break diffeomorphism invariance.

Effective Quantum Gravity in the Einstein Frame

Massive Scalar Field

Bounds on the Mass of the Massive Scalar Field

Spin-2 Massive Ghost

Conclusions and Outlook