  The Hulse-Taylor binary provides possibly the best test of GR to date. We
find the modified quadrupole formula for Infinite Derivative Gravity (IDG). We
extend the backreaction formula for propagation of gravitational waves, found
previously for Effective Quantum Gravity (EQG) for a flat background and extend
this calculation to a de Sitter background for both EQG and IDG. We put tighter
constraints on EQG using new LIGO data. We also find the power emitted by a
binary system within the IDG framework for both circular and elliptical orbits
and use the example of the Hulse-Taylor binary. IDG predicts a slightly lower
power than GR, which is exactly the observed result. We also find a lower bound
on our mass scale of $M>4.0$ keV, which is $10^6$ larger than the previous
result.
