Gravitational waves in higher-order $R^{2}$ gravity

We perform a comprehensive study of gravitational waves in the context of the higher-order quadratic scalar curvature gravity, which encompasses the ordinary Einstein-Hilbert term in the action plus an $R^{2}$ contribution and a term of the type $R\square R$. The main focus is on gravitational waves emitted by binary systems such as binary black holes and binary pulsars in the approximation of circular orbits and nonrelativistic motion. The waveform of higher-order gravitational waves from binary black holes is constructed and compared with the waveform predicted by standard general relativity; we conclude that the merger occurs earlier in our model than what would be expected from GR. The decreasing rate of the orbital period in binary pulsars is used to constrain the coupling parameters of our higher-order $R^{2}$ gravity; this is done with Hulse-Taylor binary pulsar data leading to $\kappa_{0}^{-1}\lesssim1.1\times10^{16}\,\text{m}^{2}$, where $\kappa_{0}^{-1}$ is the coupling constant for the $R^{2}$ contribution.