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

TL;DR

This paper analyzes perturbations on static, spherically symmetric backgrounds in multi-Galileon theory with N scalar fields and a linear coupling to matter, showing that enforcing stability and successful Vainshtein screening inevitably leads to either superluminal propagation or extremely slowly propagating (and thus strongly coupled) fluctuations. By formulating the quadratic fluctuation Lagrangian with the kinetic and gradient matrices K, U, V and the dispersion matrix M(q), the authors derive large- and short-distance asymptotics around a massive point source and reveal incompatible constraints: avoiding superluminality at large distances pushes the theory toward vanishing quadratic terms and loss of screening, while at short distances attempting to suppress subluminal modes induces superluminal radial modes. In the bi-Galileon case, and plausibly for general multi-Galileon theories, these tensions imply that superluminal perturbations cannot be avoided, while attempts to circumvent them lead to very low strong-coupling scales due to extremely subluminal modes; the paper thus argues that the multi-Galileon framework cannot simultaneously achieve ghost-free, stable, non-superluminal, and well-behaved perturbations under Vainshtein screening, at least for N=2 and likely for N>2 with current methods.

Abstract

We consider multi-Galileon theory, the most general Galilean invariant theory with $N$ scalar fields linearly coupled to the trace of the stress-energy tensor. We study the behavior of perturbations on a static spherically symmetric background with a massive point source, and show that, under the assumptions of stability and successful Vainshtein screening, solutions cannot be found that are free of both superluminal propagation and slowly moving, strongly coupled fluctuations. The latter imply that the theoretical and phenomenological issues related to a very low strong-interaction scale cannot be avoided in this model.