Chronology Protection in Galileon Models and Massive Gravity
  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. 
Clare Burrage, Claudia de Rham, Lavinia Heisenberg and Andrew J.   Tolley
hep-th astro-ph.CO gr-qc hep-ph