Superluminality in DGP

TL;DR

This paper demonstrates that superluminal propagation of the DGP scalar π persists on explicit stable 5D backgrounds and is not merely an artifact of the decoupling limit. By analyzing both static and time-dependent spherically symmetric brane solutions and computing the full retarded Green's function, the authors show that π signals propagate inside an enlarged light cone on the brane without instabilities, but with causality preserved in the bulk. They further show that avoiding superluminality under a purely cosmological-constant brane stress-energy is not possible within the considered parameter space, suggesting tight constraints on the DGP model and implying challenges for any UV-complete embedding. The results motivate using the absence of superluminal propagation as a constraint on infrared modifications of gravity and highlight potential obstacles for UV completions. Overall, the work clarifies the physical nature of DGP superluminality and its implications for model-building and causality in modified gravity.

Abstract

We reconsider the issue of superluminal propagation in the DGP model of infrared modified gravity. Superluminality was argued to exist in certain otherwise physical backgrounds by using a particular, physically relevant scaling limit of the theory. In this paper, we exhibit explicit five-dimensional solutions of the full theory that are stable against small fluctuations and that indeed support superluminal excitations. The scaling limit is neither needed nor invoked in deriving the solutions or in the analysis of its small fluctuations. To be certain that the superluminality found here is physical, we analyze the retarded Green's function of the scalar excitations, finding that it is causal and stable, but has support on a widened light-cone. We propose to use absence of superluminal propagation as a method to constrain the parameters of the DGP model. As a first application of the method, we find that whenever the 4D energy density is a pure cosmological constant and a hierarchy of scales exists between the 4D and 5D Planck masses, superluminal propagation unavoidably occurs.

Figures (8)

• Figure 1: Stability and superluminality of static solutions. The thick black curve is the one-parameter family of solutions discussed in the text. The upper-left white region is where the brane is inside the Schwarzschild horizon---and of course there is no static solution there.
• Figure 2: $\rho$ as a function of $r$ for static solutions.
• Figure 3: $a,\ \dot a, \ \mu$ parameter space.
• Figure 4: Examples of stable, superluminal solutions. Shown is a typical $\mu={const.}>0$ plane. The solution is confined to move along a $\rho={const.}$ contour, shown here as solid black lines for two different values of $\rho$, with arrows indicating the direction of flow. The solutions come to a 4D curvature singularity when $\ddot a = \infty$, which is exactly the boundary of the region in which $\pi$ is stable and superluminal. There is a critical value $\rho_c={3M_4^2\over 2\mu}\left(1-\sqrt{1+m^2\mu}\right)$, at which the $\rho=const.$ line bifurcates into two pieces. The leftmost line shown is for a value $\rho>\rho_c$, and the stable superluminal solution lives for only a finite proper time, going from singularity to singularity as it traverses the stable superluminal region. The rightmost line is at a value $\rho<\rho_c$, and the stable superluminal solution lives for an infinite time, extending to infinite radius. The values used for this plot are, in units of $m$, $\mu=1.5,\ \rho=\pm 0.6M_4^2$.
• Figure 5: The integration contours for the integral in $\omega$, as described in the text. The branch points are at $\omega = \pm k \equiv \pm |\vec{p}|$.