Exploring Scalarized Einstein-Gauss-Bonnet Theories Through the Lens of Parametrized Post-Newtonian Formalism

Abstract

We explore scalarized Einstein-Gauss-Bonnet theories within the context of the Parameterized Post-Newtonian formalism, which serves as a robust framework for examining modifications to General Relativity that exhibit scalarization. This approach enables us to impose a variety of constraints on the parameter space, particularly focusing on the PPN parameters $γ$ and $β$. Our analysis reveals several significant bounds for each scalarized model, utilizing data from the Cassini mission, Lunar Laser Ranging, and the forthcoming BepiColombo mission, in conjunction with geodetic Very Long Baseline Interferometry measurements around the Sun. In particular, we conducted a combined analysis of the MESSENGER mission's precision measurements of Mercury's perihelion precession $\dotω$ alongside the Cassini constraints on $γ$, yielding intriguing limits for the Ricci-EGB model. Furthermore, we investigate the impact of the new post-Newtonian potential introduced by the Gauss-Bonnet term at fourth order, which necessitates an expanded formulation of the PPN parameters. This highlights that the parameter $β$ exhibits different effects when analyzing the Ricci-EGB model. Additional constraints are derived from this framework by estimating the $γ$ PPN parameter using data from strong-lensing galaxy systems.