Exploring perturbative constraints in higher-order curvature gravity theories

Abstract 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 f ( R , R μ ν R μ ν ) 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 f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) exhibit distinctive contributions not present in GR. We assert that fundamental limitations exist, explaining why solutions of certain f ( R , R μ ν R μ ν ) models can deviate from their GR counterparts, indicating non-connected solutions or non-analytic behavior. Conversely, in the models f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) , 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.