Vainshtein Mechanism in Binary Pulsars

TL;DR

This work probes infrared modifications of gravity by calculating scalar gravitational radiation from a binary pulsar in the cubic Galileon model, leveraging the Vainshtein mechanism in the decoupling limit. The authors derive the radiation using two independent methods and decompose it into monopole, dipole, and quadrupole channels, showing that radiative suppression scales as $$(\Omega_P r_\star)^{-3/2}$$ due to the scale hierarchy with the Vainshtein radius $r_\star$, while leading monopole and dipole contributions require relativistic corrections. They find the monopole and dipole channels exist but are severely suppressed and that the quadrupole channel—though also Vainshtein-suppressed—can dominate the scalar radiation among the Galileon modes; overall, scalar radiation is at least 7–8 orders of magnitude below GR for typical DNS systems, constraining the graviton mass to $m\lesssim 10^{-27}$ eV (or $\Lambda\lesssim 10^{-9}$ eV) in this simple model. The results demonstrate that the Vainshtein mechanism remains effective in time-dependent settings and provide benchmarks for how higher-order Galileon interactions may tighten observational bounds on infrared gravity theories.

Abstract

We compute the scalar gravitational radiation from a binary pulsar system in the simplest model that exhibits the Vainshtein mechanism. The mechanism is successful in screening the effect from scalar fields conformally coupled to matter, although gravitational radiation is less suppressed relative to its general relativity predictions than static fifth forces effects within the pulsar system. This is due to a combination of two effects: firstly the existence of monopole and dipole radiation; secondly the Vainshtein suppression comes from the hierarchy of scales between the inverse frequency scale and the Vainshtein radius, rather than the orbital radius of the pulsar system. Extensions of these results will have direct relevance to infrared modifications of gravity, such as massive gravity theories, which are known to exhibit a Vainshtein mechanism. Generalization to Galileon models with higher order interactions are likely to provide stronger constraints.

Figures (1)

• Figure 1: Numerical evaluation of the the sums $\sum_{N=0}^\infty |I^M_n(e)|^2$, $\sum_{N=0}^\infty |I^D_n(e)|^2$ and $\sum_{n=0}^N |I^Q_n(e)|^2$ with $I^{M, D, Q}_n$ expressed in \ref{['IMn']}, \ref{['Idn']} and \ref{['IQn']} respectively for the eccentricity of the Hulse-Taylor pulsar 1913+16 $e=0.617$, Hulse:1974ebTaylor:1989swWeisberg:2004hi. The sums show a rapid convergence as $N\to \infty$.