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The recent direct detection of gravitational waves from a neutron star merger with optical counterpart has been used to severely constrain models of dark energy that typically predict a modification of the gravitational wave speed. However, the energy scales observed at LIGO, and the particular frequency of the neutron star event, lie very close to the strong coupling scale or cutoff associated with many dark energy models. While it is true that at very low energies one expects gravitational waves to travel at a speed different than light in these models, the same is no longer necessarily true as one reaches energy scales close to the cutoff. We show explicitly how this occurs in a simple model with a known partial UV completion. Within the context of Horndeski, we show how the operators that naturally lie at the cutoff scale can affect the speed of propagation of gravitational waves and bring it back to unity at LIGO scales. We discuss how further missions including LISA and PTAs could play an essential role in testing such models.

Such a constraint has had far-reaching consequences for models of dark energy. Within the context of the effective field theory (EFT) for dark energy

Nevertheless, it should be noted that the recent LIGO bound applies to GWs at a frequency of 10–100 Hz, while the EFT for dark energy is “constructed” as an effective field theory for describing cosmology on scales 20 orders of magnitude smaller. When it comes to constraining such EFT parameters, it is therefore important to recall that they could, in principle, depend on scale: generically, the GW speed may depend on the frequency at which it is measured,

Sound speed for

To give a precise example of how UV physics

At low frequencies with respect to the cutoff

As was the case for the scalar field theory

Turning towards future surveys, the upcoming LISA mission will have peak sensitivity near

Interestingly, in the case where

In particular, we have focused on a picture where new physics enters the low-energy EFT at a scale below

We emphasize that the aim of this work is not to revive Horndeski or any specific EFT as a particular model for dark energy. Rather the aim is to bring across the subtleties related with measurements such as the sound speed when dealing with EFTs, especially when the effective cutoff may be relatively low and comparable to the scale associated with the measurement. In the coming age of precision cosmology, correctly interpreting what EFT corrections mean for these measurements will be more important than ever before and crucial for discriminating between different classes of models.

We thank Paolo Creminelli, Lavinia Heisenberg, Atsushi Naruko, Andrew Tolley, Filippo Vernizzi, and Toby Wiseman for useful discussions. C. dR. would like to thank the Graduate Program on Physics for the Universe at Tohoku University for its hospitality during the latest stages of this work. The work of C. dR. is supported by an STFC Grant No. ST/P000762/1. C. dR. thanks the Royal Society for support at ICL through a Wolfson Research Merit Award. C. dR. is also supported in part by the European Union’s Horizon 2020 Research Council Grant No. 724659 MassiveCosmo ERC-2016-COG and in part by a Simons Foundation Award ID 555326 under the Simons Foundation’s Origins of the Universe initiative, “

The impact of Eq.

Strictly speaking, the front velocity is defined as the speed of the front of a disturbance

The argument goes through essentially unaffected if instead of Eq.

Even if the UV completion was not LI, it would be surprising that high energy physics knows about the scale of the sLB background.

In particular, this is the largest strong coupling scale, which would allow the second derivative operators

Note that the existence of higher derivative operators in this EFT should not be confused with the existence of an Ostrogradsky ghost. Indeed, higher derivative operators naturally enter from integrating out heavy degrees of freedom, and just manifest the fact that the EFT breaks down at the cutoff scale.

Note that Ref.

Horndeski models of dark energy involve many other types of other operators, which do not affect the sound speed. Including those would not affect our conclusions about

A skeptical reader may worry about an EFT with such a low cutoff of the order of

In theories that admit a Vainshtein mechanism

Interestingly, gas bounds to black holes in the LISA band may produce an x-ray signal

In addition to those that determine the background cosmological history.