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