In-depth analysis of violations of the (strong) equivalence principle in scalarized Einstein-Gauss-Bonnet theories

Abstract

We conducted a theoretical analysis of the violation of the equivalence principle within a broad class of scalar-Einstein-Gauss-Bonnet theories that exhibit spontaneous scalarization. Beginning with the Jordan frame, we performed a conformal mapping to identify the equivalent model in the Einstein frame. This approach revealed that the Gauss-Bonnet coupling introduces a mixed term that links the Einstein tensor to the kinetic terms, along with an additional kinetic term associated with the box operator, echoing characteristics of Horndeski-like theories. Our findings confirm a violation of the weak equivalence principle, as the geodesic equation incorporates an extra term that, in the non-relativistic limit, leads to a modified Newtonian equation. This result was further corroborated using Eardley's methodology. We also examined the violation of the strong equivalence principle through the Nordtvedt effect within the framework of an extended parametrized post-Newtonian (PPN) formalism. We provide a concrete example of scalarized theories featuring extended PPN parameters that deviate from general relativity, comparing these results against observational constraints from the Cassini mission, the MESSENGER mission, and the Lunar Laser Ranging experiment. While the Cassini bounds remain the most stringent, the constraints on the Nordtvedt parameter offer significantly better restrictions on the parameter space than those derived from the precession rate of Mercury's perihelion.