Evading the Vainshtein Mechanism with Anomalous Gravitational Wave Speed: Constraints on Modified Gravity from Binary Pulsars

By using observations of the Hulse-Taylor pulsar, we constrain the gravitational wave (GW) speed to the level of $10^{-2}$. We apply this result to scalar-tensor theories that generalize Galileon 4 and 5 models, which display anomalous propagation speed and coupling to matter for GWs. We argue that this effect survives conventional screening due to the persistence of a scalar field gradient inside virialized overdensities, which effectively “pierces” the Vainshtein screening. In specific branches of solutions, our result allows us to directly constrain the cosmological couplings in the effective field theory of dark energy formalism.

Figure 1

Mass-mass diagram for PSR $\mathrm{B}1913+16$ (the Hulse-Taylor pulsar) based on the post-Keplerian parameters $\dot{w}$ (black), $\gamma$ (red), and ${\dot{P}}_b$ (blue). Varying the combination $c_T{G}_{\text{gw}}/G_N$ amounts to shifting the $1\sigma$ stripe of ${\dot{P}}_b$.

Figure 2

Combined constraints in the $(c_T^2,{\alpha }_H)$ parameter space for the linear branch of solutions (14). The (tight) bound is the Cassini measurement [20] (black curve) and the light-blue stripe corresponding to the Hulse-Taylor pulsar bound obtained from the top panel. Within Horndeski theories, because $G_N=c_T^2{G}_{\text{gw}}$, the bound (6) turns into a slight preference for superluminal propagation.