Dark Energy after GW170817: dead ends and the road ahead

TL;DR

The paper demonstrates how the coincident detection of GW170817 and its EM counterparts imposes a stringent bound on the GW propagation speed, $c_g^2=1+\alpha_T$, effectively ruling out wide classes of scalar-tensor dark energy models that predict a nonzero tensor speed excess $\alpha_T$. By analyzing the tensor perturbation equation $\ddot h_{ij}+(3+\alpha_M)H\dot h_{ij}+(1+\alpha_T)k^2 h_{ij}=0$, the authors translate the observational bound into tight constraints on covariant Galileon parameters $(c_4,c_5,\xi)$ and the effective Planck mass running $\alpha_M$, leaving only a narrow, fine-tuned quintic region or simple Horndeski cases as viable late-universe DE models. They show that most quartic/quintic sectors of Horndeski and GLPV beyond-Horndeski theories are effectively excluded, while viable options reduce to (i) simple Horndeski theories with suppressed $\alpha_T$, (ii) conformally related DHOST theories preserving causality, or (iii) disformally compensated models that cancel the anomalous speed across backgrounds. The results extend to related frameworks like Einstein-Aether, Ho\v{r}ava gravity, and MOND-like theories, significantly narrowing the landscape of gravity theories for dark energy and underscoring the power of multi-messenger GW astronomy for fundamental physics.

Abstract

Multi-messenger gravitational wave (GW) astronomy has commenced with the detection of the binary neutron star merger GW170817 and its associated electromagnetic counterparts. The almost coincident observation of both signals places an exquisite bound on the GW speed $|c_g/c-1|\leq5\cdot10^{-16}$. We use this result to probe the nature of dark energy (DE), showing that a large class of scalar-tensor theories and DE models are highly disfavored. As an example we consider the covariant Galileon, a cosmologically viable, well motivated gravity theory which predicts a variable GW speed at low redshift. Our results eliminate any late-universe application of these models, as well as their Horndeski and most of their beyond Horndeski generalizations. Three alternatives (and their combinations) emerge as the only possible scalar-tensor DE models: 1) restricting Horndeski's action to its simplest terms, 2) applying a conformal transformation which preserves the causal structure and 3) compensating the different terms that modify the GW speed (to be robust, the compensation has to be independent on the background on which GWs propagate). Our conclusions extend to any other gravity theory predicting varying $c_g$ such as Einstein-Aether, Hořava gravity, Generalized Proca, TeVeS and other MOND-like gravities.

Figures (2)

• Figure 1: Left: time evolution of the tensor speed excess $\alpha_{_T}$ as a function of redshift for 300 different realizations of viable quintic Galileon cosmologies. Only quintic fine tuned cases (colored) predict $\alpha_{_T}(z=0)\approx0$. Right: 1, 2 and 3$\sigma$ confidence regions of the parameter space w.r.t. Planck+BAO for cubic (red), quartic (blue) and quintic (green) Galileons, projected on the $\alpha_{_T}(z=0),\alpha_{_M}(z=0)$ plane. Gray diagonal lines indicate the region disfavored by CMB-LSS cross correlation, measuring the ISW effect (see Renk:2017rzu for details). Models with $\alpha_{_T}<-1$ (gray filled region) have unstable tensor modes.
• Figure 2: Summary of the viable (left) and non-viable (right) scalar-tensor theories after GW170817. Only simple Horndeski theories, $G_{4,X}\approx0$ and $G_5 \approx \text{constant}$, and specific beyond Horndeski models, conformally related to $c_g=1$ Horndeski or disformally tuned, remain viable.