Chronology Protection in Galileon Models and Massive Gravity

TL;DR

The paper investigates whether Closed Time-Like Curves can form in Galileon theories and massive gravity, highlighting a two-metric causal structure in which Galileon fluctuations propagate differently from standard gravitons. It shows that while CTCs can be engineered in the naive EFT, the Galileon sector experiences infinite strong coupling and backreaction at the onset of CTCs, driving the breakdown of the EFT and preventing their formation. In the decoupling limit of ghost-free massive gravity, CTCs mirror GR-like examples, but quantum backreaction again appears before a CTC can form, enforcing Hawking-like chronology protection. If Galileons are treated as fundamental fields, CTCs can only arise through inter-species interactions across two metrics, yet those backgrounds are unstable and subject to strong coupling, preserving causality within the effective theory.

Abstract

Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in these theories it is easy to construct closed timelike curves (CTCs) within the {\it naive} regime of validity of the effective field theory. However, on closer inspection we see that the CTCs could never arise since the Galileon inevitably becomes infinitely strongly coupled at the onset of the formation of a CTC. This implies an infinite amount of backreaction, first on the background for the Galileon field, signaling the break down of the effective field theory, and subsequently on the spacetime geometry, forbidding the formation of the CTC. Furthermore the background solution required to create CTCs becomes unstable with an arbitrarily fast decay time. Thus Galileon theories satisfy a direct analogue of Hawking's chronology protection conjecture.