Superluminality in the Bi- and Multi-Galileon

Abstract

We re-explore the Bi-and Multi-Galileon models with trivial asymptotic conditions at infinity and show that propagation of superluminal fluctuations is a common and unavoidable feature of these theories, unlike previously claimed in the literature. We show that all Multi-Galileon theories containing a Cubic Galileon term exhibit superluminalities at large distances from a point source, and that even if the Cubic Galileon is not present one can always find sensible matter distributions in which there are superluminal modes at large distances. In the Bi-Galileon case we explicitly show that there are always superluminal modes around a point source even if the Cubic Galileon is not present. Finally, we briefly comment on the possibility of avoiding superluminalities by modifying the asymptotic conditions at infinity.

Superluminal vector in ghost-free massive gravity

“…5 As such, the equation of motion in Fourier space shows that the momenta of the vector fluctuations do not couple to the effective metric in front, which depends on some scalar solution φ = φ 0 (x), so their light cone remains the same as that in the flat metric. This proves that the dRGT massive gravity does not manifest superluminal vector fluctuations up to the cubic order, unlike the case with scalar fields [22]. However, (2.12) is proportional to the Maxwell equations ∂ ν F νβ = 0, which imply that the vector excitations are exactly luminal at this order.…”

“…In the decoupling limit, 2 dRGT eliminates the BoulwareDeser ghost by introducing Galileon scalar self-interaction terms for the helicity-0 mode [18,23]. In general, these Galileon terms may lead to solutions of the dRGT field equations where the scalar excitations exhibit superluminal group and phase velocities, starting from the cubic order terms onwards [18,19,22,39]. This feature is present outside the decoupling limit as well [42][43][44].…”

“…Yet many such solutions are shown to be unstable [20,21,45,46]. Also, it can be argued that the superluminality in the scalar sector of Galileon theories and massive gravity does not meddle with the usual notion of causality in local Lorentz invariant theories [22,24]. Meanwhile, as a side note, the freedom to choose the values of the two free parameters in dRGT, named c 3 and d 5 as they appear in the metric formulation [23], would circumvent the issue of scalar superluminality in the decoupling limit for a special choice of the parameters.…”

Behavior of perturbations on spherically symmetric backgrounds in multi-Galileon theory

“…[17] appeared. This paper has essentially the same scope as ours, and contains a proof of the presence of superluminal perturbations in the cubic multi-Galileon theory, as well as in the quartic bi-Galileon theory, in full agreement with our results.…”

“…In addition, Ref. [17] also studies the behavior of perturbations around a gas of particles with a given radial profile, finding that superluminal fluctuations cannot be avoided. This neatly illustrates that the phenomenon of superluminality is not a special feature of the configuration with a massive point source, but a very generic property of Galileon theories.…”