Evading the Vainshtein screen with anomalous gravitational wave speed: Constraints on modified gravity from binary pulsars

Abstract : 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 to directly constrain the cosmological couplings in the effective field theory of dark energy formalism. Introduction-Modifications of General Relativity (GR) that explain the acceleration of the Universe can display a gravitational wave (GW) speed c T = 1 (we use units = c = 1). What are the observational constraints on this parameter? In some given model, c T can be expressed as a specific function of the (post-Newtonian) parameters of the theory, and thus constrained indirectly with solar system tests (see e.g. [1]). On the other hand, cosmological observations limit c T to the 10% level (e.g. [2]). In Ref. [3], Moore and Nelson observe that sub-luminal GWs would be Cherenkov-radiated by particles traveling faster than c T. By looking at high energy cosmic rays data, the authors manage to constrain this effect to the impressive level of 10 −15. We notice, however, that the typical energy of the corresponding radiated gravi-tons, ∼ 10 10 GeV, is well above any reasonable cutoff of the modified gravity theories for cosmic acceleration. It is not difficult to envision e.g. Goldstone modes in spontaneous Lorentz breaking situations that are subluminal at low frequencies and recover relativistic propagation above the symmetry breaking scale [4]. With binary pul-sars timing data, in this letter we obtain for c T looser limits (∼ 10 −2), which however apply to frequencies that are relevant for an effective theory of dark energy. One obvious objection is that scalar tensor theories generally come equipped with screening mechanisms, allowing to recover the stringent tests of gravity in the galaxy and in the solar system. Among these, the Vain-shtein screening [5] is particularly efficient, and relevant for those scalar tensor theories that display anomalous GWs speed. What screening guarantees, however, is the suppression of the contribution of the scalar field φ to the total gravitational attraction between bodies in the Newtonian approximation. In a screened situation, the fluctuations of the metric field—gravitons—are left as the only mediators of long-range interactions. But not necessarily do they behave as in GR. The point is that the background value of the scalar φ 0 , although not directly participating in gravitational interactions, generally maintains a non vanishing gradient that spontaneously breaks Lorentz symmetry. In such a situation, the effective gravitational Lagrangian need not be that of GR, even if it involves only massless gravitons. The Vainshtein screen is pierced.
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Jose Beltrán Jiménez, Federico Piazza, Hermano Velten. Evading the Vainshtein screen with anomalous gravitational wave speed: Constraints on modified gravity from binary pulsars. Physical Review Letters, American Physical Society, 2016, 116 (6), pp.061101. 〈10.1103/PhysRevLett.116.061101 〉. 〈hal-01261103〉

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