A perturbative solution for gravitational waves in quadratic gravity

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einsteinʹs linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einsteinʹs general relativity. The perturbative solution is written as a power series in the (beta) parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency (omega), the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 < (omega) < c/|(beta)|1/2. This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin.