Dark Energy after GW170817: dead ends and the road ahead (1710.05901v2)

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, Ho\v{r}ava gravity, Generalized Proca, TeVeS and other MOND-like gravities.

• The paper establishes an ultra-tight constraint on gravitational wave speed, |c_g/c - 1| ≤ 5×10⁻¹⁶, thereby challenging many dark energy models.
• The paper demonstrates that scalar-tensor theories, especially covariant Galileon models, fail to meet the GW speed condition without fine-tuning.
• The paper outlines future directions, emphasizing multi-messenger observations to refine dark energy theories and modified gravity frameworks.

Analyzing Dark Energy Models after GW170817

The paper "Dark Energy after GW170817: Dead Ends and the Road Ahead" scrutinizes the implications of the gravitational wave event GW170817 on the theoretical landscape of dark energy models. The event GW170817 marked a significant advancement as it was accompanied by electromagnetic signals, thereby offering a unique opportunity to test the propagation speed of gravitational waves (GWs). This breakthrough enables a stringent test on various modified gravity theories that propose to explain dark energy and cosmic acceleration, particularly focusing on scalar-tensor and related modified gravity frameworks.

Key Numerical Findings

The authors establish an exceptionally tight constraint on the speed of gravitational waves relative to the speed of light, $|c_g/c-1|\leq5\cdot10^{-16}$, derived from the near-simultaneous arrival of GW170817 and its electromagnetic counterparts. This constraint is several orders of magnitude more precise than previous efforts and has profound implications for assessing the viability of numerous theoretical models.

Implications for Dark Energy Models

Applying the GW speed constraint challenges a wide array of scalar-tensor theories and other gravity models that predict a deviation in $c_g$ from $c$. Among these, the covariant Galileon model — a representative of Horndeski's theory designed to offer a self-consistent cosmological model — is substantially undermined by this new empirical evidence. The paper highlights that the covariant Galileon, known for its varying GW speed predictions, cannot be reconciled with the observed bound on $c_g$. The results effectively rule out the model for late-universe applications unless an unlikely fine-tuning is assumed.

Theoretical and Practical Implications

Horndeski theories, unless simplified, and quartic/quintic Galileons, as well as their extensions into beyond-Horndeski constructs like GLPV and DHOST, are significantly constrained or outright non-viable due to their intrinsic prediction of a non-standard GW speed. As a consequence, only minimal modifications to General Relativity satisfy the $c_g=1$ condition, making simpler scalar-tensor theories (e.g., Brans-Dicke or $f(R)$ gravity) attractive alternatives since they naturally set $c_g = c$.

Beyond Horndeski models achieve viability through either suppressing terms that modify GW speed or by implementing metric transformations that satisfy the constraint over a general background. Viable transformations include conformal changes (which do not alter causal structure) or a specifically contrived disformal transformation, both suppressing deviations from $c_g = 1$.

Future Prospects

The paper speculates on the broader theoretical landscape beyond scalar-tensor models. For instance, Einstein-Aether and Hořava-Lifshitz theories, among others, might be similarly constrained due to their predictions of varying gravitational wave speeds. Modifications involving vectors or extra dimensions in gravitational theories will face significant scrutiny in light of the GW170817 findings.

The paper concludes that while the detection of GW170817 has imposed a challenging hurdle for many theoretical approaches to dark energy, it simultaneously offers clarity in narrowing the viable paths for future theoretical developments. Future multi-messenger observations will further refine these limits and aid in the selection of realistic models of dynamical dark energy and modifications to General Relativity.

By critically evaluating the consequences of multi-messenger signals from astrophysical events, the paper emphasizes that the constructive interplay of observational data and theoretical modeling is crucial in understanding the universe's accelerated expansion. Future observational endeavors will likely continue to constrain or endorse the real-world applicability of diverse theoretical models, thereby steering the course of cosmic physics and gravitation studies.