Superluminality in the Bi- and Multi- Galileon

TL;DR

This work shows that Bi- and Multi-Galileon theories with trivial asymptotics inherently support superluminal fluctuations. It demonstrates that any Cubic Galileon term yields large-distance superluminality from a point source, and even without Cubic terms, certain matter distributions induce superluminal modes; near a point source, Quartic Bi-Galileon interactions also generate superluminal propagation. The results reveal a no-go aspect: the Vainshtein mechanism in these theories is generically accompanied by superluminalities under physically reasonable stability and boundary conditions. A possible escape lies in nontrivial asymptotic boundary conditions, as in some massive gravity realizations, but within the standard Galileon framework with trivial infinity, superluminalities appear unavoidable and are tied to the theory’s causal structure rather than to acausal pathologies like closed timelike curves. The findings align with other analyses suggesting chronology protection-type constraints and motivate further exploration of boundary-condition choices in modified gravity models.

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.