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Stability and superluminality of spherical DBI galileon solutions

Garrett L. Goon, Kurt Hinterbichler, Mark Trodden

TL;DR

The paper investigates stability and signal propagation in DBI galileon theories by deriving static spherical solutions sourced by a point mass, performing a perturbative stability analysis, and computing the speeds of small fluctuations. The authors show ghost-free, stable spherical backgrounds exist for a parameter region with $d_2>0$, $d_4> M/(8\pi)$, $d_3\ge\sqrt{(3/2)d_2d_4}$, and $d_5\le (3/4)d_4^2/d_3$, but the radial mode propagates superluminally at large distances while angular modes remain subluminal. This persistent superluminality challenges the existence of a Lorentz-invariant UV completion and motivates further work on covariant formulations or modified couplings to gravity. The analysis also clarifies how the scales $d_2$ and $d_4$ set strong-coupling and interaction strengths, with implications for embedding DBI galileons in gravitational contexts. Overall, the work extends the understanding of DBI galileons, highlighting a tension between stability and subluminal propagation that mirrors issues found in ordinary galileons.

Abstract

The DBI galileons are a generalization of the galileon terms, which extend the internal galilean symmetry to an internal relativistic symmetry, and can also be thought of as generalizations of DBI which yield second order field equations. We show that, when considered as local modifications to gravity, such as in the Solar system, there exists a region of parameter space in which spherically symmetric static solutions exist and are stable. However, these solutions always exhibit superluminality, casting doubt on the existence of a standard Lorentz invariant UV completion.

Stability and superluminality of spherical DBI galileon solutions

TL;DR

The paper investigates stability and signal propagation in DBI galileon theories by deriving static spherical solutions sourced by a point mass, performing a perturbative stability analysis, and computing the speeds of small fluctuations. The authors show ghost-free, stable spherical backgrounds exist for a parameter region with , , , and , but the radial mode propagates superluminally at large distances while angular modes remain subluminal. This persistent superluminality challenges the existence of a Lorentz-invariant UV completion and motivates further work on covariant formulations or modified couplings to gravity. The analysis also clarifies how the scales and set strong-coupling and interaction strengths, with implications for embedding DBI galileons in gravitational contexts. Overall, the work extends the understanding of DBI galileons, highlighting a tension between stability and subluminal propagation that mirrors issues found in ordinary galileons.

Abstract

The DBI galileons are a generalization of the galileon terms, which extend the internal galilean symmetry to an internal relativistic symmetry, and can also be thought of as generalizations of DBI which yield second order field equations. We show that, when considered as local modifications to gravity, such as in the Solar system, there exists a region of parameter space in which spherically symmetric static solutions exist and are stable. However, these solutions always exhibit superluminality, casting doubt on the existence of a standard Lorentz invariant UV completion.

Paper Structure

This paper contains 6 sections, 44 equations, 1 figure.

Table of Contents

  1. Introduction
  2. DBI galilean terms and equations of motion
  3. Spherical solutions
  4. Stability
  5. Propagation speed of fluctuations
  6. Conclusions

Figures (1)

  • Figure 1: Speed of fluctuations $c_r^2$ and $c_\Omega^2$, in the radial and angular directions respectively, for a sample solution satisfying the existence and stability constraints (\ref{['finalconstraints']}), as well as (\ref{['subluminalconstraint']}). The values chosen are $d_2=1$, $d_3=2$, $d_4=1$, $d_5=-1$, $M=1$.