Constraints on Born-Infeld gravity from the speed of gravitational waves after GW170817 and GRB 170817A

TL;DR

This paper uses gravitational wave and gamma-ray burst observations from GW170817 and GRB 170817A to constrain the parameters of Eddington-inspired Born-Infeld gravity, focusing on the deviation of gravitational wave speed from light speed.

Contribution

It provides the first direct observational bounds on the EiBI gravity parameter using gravitational wave and electromagnetic signals.

Findings

Bound on EiBI parameter from Earth-based detector time delay: |κ| ≲ 10^{21} m^2.

Bound from cosmological background analysis: |κ| ≲ 10^{37} m^2.

Bounds are weaker than other astrophysical constraints but are directly observational.

Abstract

The observations of gravitational waves from the binary neutron star merger event GW170817 and the subsequent observation of its electromagnetic counterparts from the gamma-ray burst GRB 170817A provide us a significant opportunity to study theories of gravity beyond general relativity. An important outcome of these observations is that they constrain the difference between the speed of gravity and the speed of light to less than $10^{-15}c$. Also, the time delay between the arrivals of gravitational waves at different detectors constrains the speed of gravity at the Earth to be in the range $0.55c < v_{gw} < 1.42c$. We use these results to constrain a widely studied modified theory of gravity: Eddington-inspired Born-Infeld (EiBI) gravity. We show that, in EiBI theory, the speed of gravitational waves in matter deviates from $c$. From the time delay in arrival of gravitational wave signals at Earth-based detectors, we obtain the bound on the theory parameter $\kappa$ as $\vert\kappa\vert \lesssim 10^{21}\, m^2$. Similarly, from the time delay between the signals of GW170817 and GRB 170817A, in a background Friedmann-Robertson-Walker universe, we obtain $\vert \kappa \vert \lesssim 10^{37}\, m^2$. Although the bounds on $\kappa$ are weak compared to other earlier bounds from the study of neutron stars, stellar evolution, primordial nucleosynthesis, etc., our bounds are from the direct observations and thus worth noting.