[Paper Review] Gravitational wave speed: Implications for models without a mass scale

Henrik Nersisyan, Nelson A. Lima+1 more|arXiv (Cornell University)|Jan 20, 2018

Geophysics and Gravity Measurements3 citations

TL;DR

This paper demonstrates that modified gravity models without an additional mass scale—such as Brans-Dicke, nonlocal theories, and Galileon models—can evade constraints from gravitational wave speed measurements because their gravitational slip parameter η becomes scale-independent and unconstrained by cT = c. While standard Horndeski models are tightly restricted by GW observations, these scale-free theories maintain η ≠ 1 without violating the speed-of-gravity constraint.

ABSTRACT

The recent report that the gravitational wave speed equals the light speed puts strong constraints on the anisotropic stress parameter of many modified gravity models, a quantity that is directly observable through large-scale structure. We show here that models without a mass scale completely escape these constraints. We discuss a few relevant cases in detail: Brans-Dicke theory, nonlocal models, and Galileon Lagrangian.

Motivation & Objective

• To investigate whether modified gravity models without a new mass scale can evade the stringent constraint on gravitational wave speed cT = c.
• To analyze how the absence of a mass scale affects the gravitational slip parameter η and its scale dependence in modified gravity theories.
• To evaluate the observational viability of scale-free models such as Brans-Dicke, nonlocal gravity, and Galileon theories in light of GW constraints.
• To clarify the distinction between models with and without a mass scale in their response to the GW speed constraint.
• To argue that η remains a key observable parameter for testing modified gravity even after the cT = c measurement.

Proposed method

• Analyzes the gravitational slip parameter η = −Φ/Ψ in the quasi-static approximation for modified gravity models.
• Applies the constraint |cT/c − 1| ≤ 1×10−15 from the GW170817 neutron star merger to Horndeski and related theories.
• Identifies that models without a new mass scale (beyond the Planck scale) exhibit scale-independent η, decoupled from cT constraints.
• Examines Brans-Dicke theory in the Jordan frame, showing cT = c but η ≠ 1, unconstrained by GW data.
• Studies nonlocal gravity models (e.g., DW model), confirming cT = c and scale-independent η without mass scale dependence.
• Analyzes Galileon Lagrangians with shift symmetry, showing that cT = c forces c4 = c5 = 0, collapsing to GR with η = 1, but otherwise η is scale-independent and unconstrained.

Experimental results

Research questions

• RQ1 Can modified gravity models without a new mass scale evade the gravitational wave speed constraint cT = c?
• RQ2 How does the absence of a mass scale affect the scale dependence and observational constraints on the gravitational slip parameter η?
• RQ3 Why are Horndeski models with a mass scale ruled out by GW observations, while scale-free models remain viable?
• RQ4 What is the role of the Galileon symmetry in determining the gravitational wave speed and η in nonlocal theories?
• RQ5 To what extent can η remain a non-trivial, observable parameter in modified gravity after the cT = c measurement?

Key findings

• Models without a new mass scale, such as Brans-Dicke and nonlocal gravity, predict cT = c but allow η to be scale-independent and different from unity.
• In the quasi-static approximation, the gravitational slip parameter η is scale-independent in theories without a mass scale, unlike in Horndeski models with a mass scale.
• For Galileon theories, the requirement cT = c forces the coefficients c4 = c5 = 0, reducing the theory to General Relativity with η = 1, making it trivial.
• The constraint |cT/c − 1| ≤ 1×10−15 does not constrain η in scale-free models because η is independent of the GW speed in these cases.
• The gravitational slip parameter η remains a viable and informative observable for testing modified gravity, even after the GW170817 constraint.
• Theories with shift symmetry (e.g., Galileon) or conformal coupling (e.g., Brans-Dicke) avoid GW constraints not due to cT ≠ c, but due to the absence of a mass scale in the perturbation equations.