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

Martín G. Richarte, Júnior D. Toniato

TL;DR

This work analyzes violations of the weak and strong equivalence principles in a broad class of scalarized Einstein-Gauss-Bonnet theories by moving between the Jordan and Einstein frames and employing Eardley’s approach to test-mass motion. It reveals Horndeski-like couplings and nonlinear kinetic terms in the Einstein-frame action, leading to composition-dependent geodesics and a nonconserved energy-momentum tensor that signals WEP and SEP violations. The authors develop an extended post-Newtonian framework with dual parameters $β_1$ and $β_2$ and a Nordtvedt parameter $η_N$ to describe SEP violations and periastron precession, and they confront these predictions with Cassini, MESSENGER, and LLR data. The results show that Cassini provides the strongest bounds on the PPN γ parameter, while Nordtvedt-based constraints significantly tighten the sEGB parameter space, motivating further 2PN analyses and new tests with triple systems or atomic clocks to sharpen the empirical limits on these scalarized gravity models.

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.

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

TL;DR

This work analyzes violations of the weak and strong equivalence principles in a broad class of scalarized Einstein-Gauss-Bonnet theories by moving between the Jordan and Einstein frames and employing Eardley’s approach to test-mass motion. It reveals Horndeski-like couplings and nonlinear kinetic terms in the Einstein-frame action, leading to composition-dependent geodesics and a nonconserved energy-momentum tensor that signals WEP and SEP violations. The authors develop an extended post-Newtonian framework with dual parameters and and a Nordtvedt parameter to describe SEP violations and periastron precession, and they confront these predictions with Cassini, MESSENGER, and LLR data. The results show that Cassini provides the strongest bounds on the PPN γ parameter, while Nordtvedt-based constraints significantly tighten the sEGB parameter space, motivating further 2PN analyses and new tests with triple systems or atomic clocks to sharpen the empirical limits on these scalarized gravity models.

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.

Paper Structure

This paper contains 8 sections, 58 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Scalarized Einstein-Gauss-Bonnet theories
  3. Jordan frame
  4. Einstein frame
  5. Equivalence Principle
  6. The Nordtvedt effect and observational constraints
  7. summary
  8. Acknowledgments

Figures (1)

  • Figure 1: In the Ricci-EGB model, we present the combined constraints on the parameter $\gamma$ based on data from the Cassini mission and MESSENGER observations regarding the precession rate of Mercury's perihelion. This is complemented by measurements on the Nordtvedt parameter from LLR (left) and MESSENGER (right).