Gravitational waves from inspiraling black holes in quadratic gravity

We perform a study of gravitational waves emitted by inspiraling black holes in the context quadratic gravity. By linearizing field equations around flat background, we demonstrate that all degrees freedom satisfy wavelike equations. These split into three modes: massive spin-2 mode, spin-0 and expected massless mode. construct energy-momentum tensor show that, due to it presents Ostrogradsky instability. also how deal with this possible pathology obtain consistent physical interpretations for system. Using tensor, influence each mode orbital dynamics compare standard result general relativity. Moreover, present two methods constrain parameter $\ensuremath{\alpha}$ associated contribution. From first method, using combined waveform modes, constraint $\ensuremath{\alpha}\ensuremath{\lesssim}1.1\ifmmode\times\else\texttimes\fi{}{10}^{21}\text{ }\text{ }{\mathrm{m}}^{2}$. In second coalescence time, get $\ensuremath{\alpha}\ensuremath{\lesssim}1.1\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{