Parameterized post-Newtonian analysis of quadratic gravity and solar system constraints

Abstract This work systematically investigates the post-Newtonian behavior of general quadratic gravity in the weak-field regime. By extending the Einstein–Hilbert action to include quadratic curvature terms as L R- C²+ R² L ∝ R - λ C 2 + μ R 2, the theory introduces two massive modes: a scalar mode and a ghost tensor mode. Using the post-Newtonian expansion method, we derive the explicit expressions for the metric for a general source up to 1. 5PN order. Furthermore, for a point-mass source, we extend the solution to 2PN order and evaluate the effective parameterized post-Newtonian parameters (r) γ (r) and (r) β (r). The results show that deviations from General Relativity are exponentially suppressed. The theory has the feature (r) 1 γ (r) ≡ 1 when mR=mW m R = m W, and to ensure that gravity remains attractive, we have mW>mR/4 m W > m R / 4. At short distance scales, the Newtonian potential no longer exhibits a 1/ r behavior, but instead displays a polynomial dependence on r. The leading correction to (r) β (r) exhibiting a characteristic O (r (r) e^-mr) O (r ln (r) e - m r) dependence. Based on the Solar System experiments, we derive preliminary constraints on the theory’s parameters: mR, mW 23 ~AU^-1 m R, m W ≳ 23 AU - 1, corresponding to 2. 1 10^19 ~m² λ