A perturbative solution for gravitational waves in quadratic gravity

Abstract

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein&#39;s linearized field equations. We show that only the Ricci squared quadratic invariant contributes to give a different solution of those found in Einstein&#39;s general relativity. The perturbative solution is written as a power series in the $β$ 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 $ω$, the perturbative solution can be summed out to give an exact solution to linearized version of quadratic gravity, for $0<ω<c/\midβ\mid^{1/2}$. This result may lead to implications to the predictions for gravitational wave backgrounds of cosmological origin.