Causality Constraints on Massive Gravity

TL;DR

This work analyzes causality constraints in 4D $dRGT$ massive gravity by constructing pp-wave backgrounds and studying linear fluctuations. Through an explicit analysis of Shapiro-like time shifts for longitudinal modes, the authors show that measurable time advances occur for all parameter values within the effective field theory regime, and that closed timelike curves can form outside a critical line $\alpha_3 = -\tfrac{1}{2}$. The results identify a causality-bound region, align with UV-completion considerations (Cheung–Remmen island), and illustrate IR manifestations of fundamental consistency requirements in massive gravity. Overall, the paper constrains the $\alpha_3$–$\alpha_4$ parameter space by linking causality, EFT validity, and UV completion ideas.

Abstract

The de Rham-Gabadadze-Tolley massive gravity admits pp-wave backgrounds on which linear fluctuations are shown to undergo time advances for all values of the parameters. The perturbations may propagate in closed time-like curves unless the parameter space is constrained to a line. These classical phenomena take place well within the theory's validity regime.

Figures (4)

• Figure 1: Profiles of the sandwich wave: $u$-direction profile (left) and radial profile in the transverse plane (right).
• Figure 2:
• Figure 3: Motion of a probe that follows a CTC, projected on the $u$-$v$ plane (left) and on the transverse plane (right).
• Figure 4: A cartoon of the Cheung-Remmen parameter island. The red line $c_3=1/4$ corresponds to our result $\alpha_3=-1/2$.