A perturbative solution for gravitational waves in quadratic gravity

TL;DR

This paper derives a perturbative gravitational wave solution in quadratic gravity, showing how Ricci squared terms modify Einstein's solutions and providing an exact solution for certain wave frequencies.

Contribution

It introduces a perturbative approach to solve linearized quadratic gravity and sums it to an exact solution for specific wave frequencies.

Findings

Ricci squared invariant alters gravitational wave solutions

Perturbative series can be summed for monochromatic waves

Exact solutions are valid for frequencies below a certain threshold

Abstract

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to give a different solution of those found in Einstein's 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 linearized version of quadratic gravity, for $0<\omega<c/\mid\beta\mid^{1/2}$. This result may lead to implications to the predictions for gravitational wave backgrounds of cosmological origin.