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Closed Timelike Curves in the Galileon Model

Jarah Evslin, Taotao Qiu

TL;DR

The paper shows that closed timelike curves can arise in Galileon models in Minkowski space by constructing a configuration where perturbations propagate with an effective metric $G^{\mu\nu}=\eta^{\mu\nu}-\partial^\mu\partial^\nu\phi_0$ and certain higher-derivative dominance conditions (e.g., $h=-f''$ with $h>1$) enable backward-in-time signaling. It starts with a single cylindrical bar and demonstrates how boundary rods can enforce traversal that, when combined with additional bars arranged in a polygon, yields a CTC; the construction also analyzes boundary conditions, stability (no local ghosts at $r=0$ under the chosen setup), and the impact of quantum corrections through perturbativity parameters $\alpha_q^{(1)}$ and $\alpha_q^{(2)}$. A key result is that CTCs can exist within the Galileon EFT, but their realization is frame-dependent regarding EFT validity, highlighting nonlocal constraints on initial data and potential limits of the EFT as a UV completion. Overall, the work emphasizes that superluminality alone is not pathological, but CTCs in Galileon theories expose nuanced questions about nonlocal consistency, EFT validity, and the role of UV completion in higher-derivative scalar theories.

Abstract

It has long been known that generic solutions to the nonlinear DGP and Galileon models admit superluminal propagation. In this note we present a solution of these models which also admits closed timelike curves (CTCs). We observe that these CTCs only arise when, according to each observer, there exists some region in which the higher derivative terms are larger than the 2-derivative kinetic term.

Closed Timelike Curves in the Galileon Model

TL;DR

The paper shows that closed timelike curves can arise in Galileon models in Minkowski space by constructing a configuration where perturbations propagate with an effective metric and certain higher-derivative dominance conditions (e.g., with ) enable backward-in-time signaling. It starts with a single cylindrical bar and demonstrates how boundary rods can enforce traversal that, when combined with additional bars arranged in a polygon, yields a CTC; the construction also analyzes boundary conditions, stability (no local ghosts at under the chosen setup), and the impact of quantum corrections through perturbativity parameters and . A key result is that CTCs can exist within the Galileon EFT, but their realization is frame-dependent regarding EFT validity, highlighting nonlocal constraints on initial data and potential limits of the EFT as a UV completion. Overall, the work emphasizes that superluminality alone is not pathological, but CTCs in Galileon theories expose nuanced questions about nonlocal consistency, EFT validity, and the role of UV completion in higher-derivative scalar theories.

Abstract

It has long been known that generic solutions to the nonlinear DGP and Galileon models admit superluminal propagation. In this note we present a solution of these models which also admits closed timelike curves (CTCs). We observe that these CTCs only arise when, according to each observer, there exists some region in which the higher derivative terms are larger than the 2-derivative kinetic term.

Paper Structure

This paper contains 6 sections, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Galileon Models
  3. A Galileon Configuration with a CTC
  4. A single bar
  5. Robustness of the cylinder solution
  6. Assembling rods to make a configuration with CTCs

Figures (2)

  • Figure 1: Two rods pass each other with a finite impact parameter. A potential CTC threads the two rods along the direction of their motion, traveling backwards in time as it travels through each. However during the time required to travel between the rods, the inter-rod interactions are likely to destroy the configuration.
  • Figure 2: A configuration is considered in which $n$ rods form a clockwise-moving $n$-gon. Now, for a fixed rod radius, the time required by the perturbation to travel from the core of one rod to the next may, for some value of $n$ be arbitrarily small. Therefore the interactions between the rods during this time interval may be neglected.