QED and the flat space Galileon are considered as examples of low energy EFTs with superluminal signals. In QED, on all backgrounds the superluminal signal advance is always smaller than the distance resolved by the EFT (the inverse electron mass), so this apparent superluminality is not problematic. For the Galileon, there are many backgrounds on which the superluminal signal advance is parametrically larger than the resolving power of the EFT (the Vainshtein radius), which means that any consistent (subluminal) UV completion must contain quantum corrections which are important at the Vainshtein radius.

Demanding subluminal signal speeds is a common 'consistency condition' imposed when constructing low energy effective field theories. However, there has been much discussion over whether a speed of sound c_s >1 is enough to actually violate causality, or lead to any kind of inconsistency. Here we have a good account of the cases of QED and the flat-space Galileon, clearly demonstrating that superluminality is only truly fatal for a theory if its effects can be resolved within the EFT regime of validity.

Perturbing the quartic Galileon to quadratic order, the 'inverse method' is used to construct solutions which contain a non-singular bounce which is free of instabilities and superluminality. Specifically, one postulates a desired background solution, potential, and kinetic coefficients of the tensor sector (H(t), ϕ(t), dϕ/dt, V (t), A_h(t), B_h(t)) and then determines how all of the couplings must evolve in order for this to be a bonafide solution of the equations of motion. Previously, with just a cubic Galileon, one had only been able to postulate (H(t), dp/dt, V (t)), and there was invariably an instability at some finite time before the bounce.

This latest installment in a series of papers on whether a single scalar field on an FRW background can induce a classically stable bounce argues that by including the Galileon terms L₂, L₃, L₄, one has enough freedom in choosing the three free functions (of the scalar and its first derivative) to ensure that there are no ghosts, gradient instabilities, or superluminal propagation for the whole time evolution. Without L₄, one can only arrange for these conditions to be met within the window of Null Energy Condition violation, but will generally encounter instabilities at earlier or later times.