Weak field limit and gravitational waves in higher-order gravity

Abstract

We derive the weak field limit for a gravitational Lagrangian density [Formula: see text], where higher-order derivative terms in the Ricci scalar [Formula: see text] are taken into account. The interest for this kind of effective theories comes out from the consideration of the infrared and ultraviolet behaviors of gravitational field and, in general, from the formulation of quantum field theory in curved spacetimes. Here, we obtain solutions in weak field regime both in vacuum and in the presence of matter and derive gravitational waves considering the contribution of [Formula: see text] terms. By using a suitable set of coefficients [Formula: see text], it is possible to find up to [Formula: see text] normal modes of oscillation with six polarization states with helicity 0 or 2. Here [Formula: see text] is the higher-order term in the [Formula: see text] operator appearing in the gravitational Lagrangian. More specifically: the mode [Formula: see text], with [Formula: see text], has transverse polarizations [Formula: see text] and [Formula: see text] with helicity 2; the [Formula: see text] modes [Formula: see text], with [Formula: see text], have transverse polarizations [Formula: see text] and non-transverse ones [Formula: see text], [Formula: see text], [Formula: see text] with helicity 0.