Cosmological axial gravitational waves in the f ( R ) Starobinsky model

We investigate the propagation of cosmological axial (or odd parity) gravitational waves (GWs) in the framework of the f ( R ) gravity with f(R) = R+λ R^2 , the Starobinsky model. The metric tensor and the energy–momentum tensor of matter are perturbed by using the Regge–Wheeler axial perturbations framework. We solve the coupled system of differential equations of the perturbation parameters for two cosmological eras in which simply analytical solutions can be found, namely the radiation-dominated epoch and the de Sitter stage. In the former case, the Starobinsky model predicts exactly the same result of the General Relativity theory. On the other hand, remembering that in the Starobinsky inflation, the Universe starts within a metastable de Sitter state, we find the evolution of the axial GWs for this early epoch. In this sense, our results should be interpreted as the initial conditions for axial GWs in the Starobinsky model. We show how the initial evolution of axial GWs is affected by the presence of the higher-order curvature term and how it depends on the model parameter λ . Certainly, such an effect could leave an imprint on the spectrum of axial GWs at the end of the Starobinsky inflation, but this is a subject of further investigations.