Exploring perturbative constraints in higher-order curvature gravity theories

In the realm of general relativity (GR) and extended theories of gravity, obtaining solutions for scenarios of physical interest is a highly intricate challenge. By employing the formalism of mathematical perturbation theory within the GR framework, we demonstrate that, for a significant class of vacuum theories, the corresponding solutions do not yield additional effects beyond those predicted by GR’s perturbation theory. However, models characterized by terms of the form exhibit distinctive contributions not present in GR. We assert that fundamental limitations exist, explaining why solutions of certain models can deviate from their GR counterparts, indicating non-connected solutions or non-analytic behavior. Conversely, in the models , the solutions seamlessly connect with those of GR. This distinction highlights the nuanced interplay between higher-order curvature terms and their impact on gravitational dynamics, offering new insights into the landscape of modified gravity theories.