Gravitational Rainbows: LIGO and Dark Energy at its Cutoff

Abstract

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. Dark Energy after GW170817 and GRB170817A:The recent direct detections of gravitational waves (GWs) have had an unprecedented impact on our understanding of gravity at a fundamental level. The first event alone (GW150914 [1]) was already sufficient to put bounds on the graviton with better precision than what we know of the photon. Last year, the first detection of GWs from a neutron star merger (GW170817), some 10 15 light seconds away, which arrived within one second of an optical counterpart (GRB170817A), allowed us to constrain the GW speed with remarkable precision [2-4]with c T the GW phase velocity and c γ the speed of light.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 [5], it was rapidly pointed out that (1) was sufficient to suppress the EFT operators that predict non-luminal gravitational propagation [6][7][8][9][10][11][12][13][14]. In particular, within the framework of scalar-tensor theories of gravity, Horndeski [15] has played a major part in the past decade as a consistent ghost-free EFT in which the scalar degree of freedom could play the role of dark energy. Yet the interplay between the scalar and gravity typically implies that GWs would not travel luminally. The LIGO constraint on the GW speed only leaves out the generalization of the cubic Galileon [16], which is severely constrained by other observations. As a result the Horndeski EFT seems almost entirely ruled out as a dark energy candidate [17].Nevertheless, it should be noted that the recent LIGO bound applies to GWs at a frequency of 10 − 100Hz, 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

Phenomenology of the generalized cubic covariant Galileon model and cosmological bounds

“…In this regards the EFT parameters could be dependent on the energy scale in such a way that their values measured at low-energy scales may receive corrections when approaching larger frequency. Indeed, the latter has been shown to be the case of the tensor speed of propagation [95]. Furthermore, the results of [94] seems to imply that we cannot neglect higher order perturbations terms compared to lower order ones.…”

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

“…The almost coincident measurements of gravitational waves (GWs) emitted from a binary NS merger by LIGO and its associated short gamma-ray burst [44][45][46][47][48][49][50] suggest that the difference between the speed of GWs c gw and the speed of light c is at most of O(10 −15 ). Theories compatible with the condition c g = c on cosmological scales have to satisfy A 1 = A 2 = 0 (see also [51]). Further constraints on DHOST theories are imposed in terms of graviton decay into dark energy [14], which put A 3 = 0.…”

Black hole ringdown as a probe for dark energy

“…where we used Eqs. (19) and (14). Notice that the way this effect scales with distances and masses of the systems is only dependent on the choice of the dominant operator (i.e.…”

“…In particular, both the estimations for the scalar background and the size of the mixing are then given by the same expressions as for black holes, Eqs. (14) and (19) respectively, appropriately substituting r s by r ⊕ s . We will assume this is the case, and we will later check that this is indeed satisfied for specific choices of α, Λ and the form of the leading HD operator (n and m).…”

“…In this paper instead we will follow a different route. We will assume that the UV cutoff of the dark energy EFT, and 3 Note that the frequencies of the LIGO measurement of GW170817 are close to Λ 3 , so additional assumptions about the UV physics are implicitly made when using this measurement to constrain such 'cosmological' operators suppressed by Λ 3 [19]. 4 The exact definition of the operators is given below in Eq.…”