Constraints on scalar-tensor theory of gravity by the recent observational results on gravitational waves

TL;DR

This paper uses recent gravitational wave observations to place constraints on scalar-tensor theories of gravity, particularly Horndeski models, limiting coupling strengths and mass scales to ensure compatibility with GW speed measurements.

Contribution

It provides new bounds on the coupling parameters and mass scales in Horndeski theories based on gravitational wave speed constraints from GW170817.

Findings

Gauss-Bonnet coupling constrained to ~10^{-15}

Mass scale M in Horndeski theory constrained between 10^{15} GeV and 2×10^{-35} GeV

Non-minimal derivative coupling effects are negligible at late times

Abstract

The speed of gravitational waves provides us a new tool to test alternative theories of gravity. The constraint on the speed of gravitational waves from GW170817 and GRB170817A is used to test some classes of Horndeski theory. In particular, we consider the coupling of a scalar field to Einstein tensor and the coupling of the Gauss-Bonnet term to a scalar field. The coupling strength of the Gauss-Bonnet coupling is constrained to be in the order of $10^{-15}$. In the Horndeski theory we show that in order for this theory to satisfy the stringent constraint on the speed of GWs the mass scale $M$ introduced in the non-minimally derivative coupling is constrained to be in the range $10^{15}\text{GeV}\gg M \gtrsim 2\times 10^{-35}$GeV taking also under consideration the early times upper bound for the mass scale $M$. The large mass ranges require no fine-tuning because the effect of non-minimally derivative coupling is negligible at late times.