Causality constraints in Quadratic Gravity

TL;DR

This paper investigates the causality constraints of Quadratic Gravity using shock wave solutions, demonstrating that it remains causal with positive, polarization-independent graviton time delays, despite additional modes.

Contribution

It extends CEMZ causality constraints analysis to Quadratic Gravity in shock wave backgrounds, confirming its causality beyond general relativity.

Findings

Graviton Shapiro time delay is polarization-independent and positive.

Quadratic Gravity satisfies CEMZ causality constraints.

Additional propagating modes do not violate causality.

Abstract

Classifying consistent effective field theories for the gravitational interaction has recently been the subject of intense research. Demanding the absence of causality violation in high energy graviton scattering processes has led to a hierarchy of constraints on higher derivative terms in the Lagrangian. Most of these constraints have relied on analysis that is performed in general relativistic backgrounds, as opposed to a generic solution to the equations of motion which are perturbed by higher curvature operators. Hence, these constraints are necessary but may not be sufficient to ensure that the theory is consistent. In this context, we explore the so-called CEMZ causality constraints on Quadratic Gravity in a space of shock wave solutions beyond GR. We show that the Shapiro time delay experienced by a graviton is polarization-independent and positive, regardless of the strength of the gravitational couplings. Our analysis shows that as far as the causality constraints are concerned, albeit inequivalent to General Relativity due to additional propagating modes, Quadratic Gravity is causal as per as the diagnostic proposed by CEMZ.