[Paper Review] Tests of Gravitation at Solar System scales beyond the PPN formalism

Aurélien Hees, W. M. Folkner+5 more|arXiv (Cornell University)|Mar 6, 2014

Geophysics and Gravity Measurements5 references3 citations

TL;DR

This paper presents new constraints on alternative gravity theories beyond the standard PPN formalism using Cassini and Messenger spacecraft data. It tests the Standard Model Extension (SME) for Lorentz symmetry violations and the External Field Effect in MOND using Doppler and range tracking data, finding no evidence for deviations from General Relativity and excluding standard MOND models with 95% confidence.

ABSTRACT

In this communication, the current tests of gravitation available at Solar System scales are recalled. These tests rely mainly on two frameworks: the PPN framework and the search for a fifth force. Some motivations are given to look for deviations from General Relativity in other frameworks than the two extensively considered. A recent analysis of Cassini data in a MOND framework is presented. Furthermore, possibilities to constrain Standard Model Extension parameters using Solar System data are developed.

Motivation & Objective

• To explore alternative frameworks for testing gravity beyond the widely used PPN formalism and fifth-force models.
• To assess the sensitivity of existing Solar System data—specifically Cassini and Messenger radio tracking data—to constraints on Lorentz symmetry violations in the gravitational sector via the SME framework.
• To test the viability of the MOND phenomenology, particularly the External Field Effect (EFE), using high-precision Cassini tracking data.
• To improve limits on SME coefficients and constrain MOND interpolating functions using state-of-the-art data analysis techniques.

Proposed method

• Utilizes Doppler and range measurements from Cassini and Messenger space missions to model spacecraft trajectories and extract gravitational anomalies.
• Applies a modified orbital fitting procedure that omits range data from trajectory estimation to preserve range residuals for detecting potential deviations.
• Introduces a parametrized correction to the Newtonian potential to model the MOND External Field Effect (EFE), characterized by the parameter $ Q_2 $.
• Performs a joint fit of planetary orbits, solar mass, EFE parameter $ Q_2 $, and calibration terms (radio delay, plasma model) to isolate gravitational effects.
• Estimates uncertainties on SME coefficients using linear combinations derived from the data, leveraging the sensitivity of radio tracking to spacetime metric deviations.
• Uses a statistical analysis of residuals to test for systematic deviations consistent with alternative gravity models.

Experimental results

Research questions

• RQ1 Can existing Cassini and Messenger radio tracking data constrain Lorentz symmetry violations in the gravitational sector as described by the SME framework?
• RQ2 What are the estimated uncertainties on SME coefficients $ \bar{s}_{\mu\nu} $ achievable with current Solar System data?
• RQ3 Is there measurable evidence for the MOND External Field Effect in the Saturn system using Cassini tracking data?
• RQ4 How do the constraints from Cassini data compare to theoretical predictions for standard MOND interpolating functions?
• RQ5 Can the inclusion of Doppler-only data improve sensitivity to long-wavelength gravitational anomalies compared to full-range-and-Doppler fits?

Key findings

• The estimated uncertainty on the SME coefficient $ \bar{s}_C $ is $ 3.2 \times 10^{-11} $, and on $ \bar{s}_A $ is $ 1.1 \times 10^{-10} $, indicating high sensitivity to Lorentz violation.
• For Cassini data, the uncertainty on $ \bar{s}_H $ is $ 2.3 \times 10^{-11} $, and on $ \bar{s}_F $ is $ 8.6 \times 10^{-11} $, demonstrating strong constraints on SME parameters.
• The MOND EFE parameter $ Q_2 $ is constrained to $ (3 \pm 3) \times 10^{-27} \, \text{s}^{-2} $, with $ Q_2 = 0 $ within the 1-\sigma confidence interval.
• The result excludes standard MOND models with interpolating functions $ \mu_{1,2} $, $ \mu_{\rm exp} $, and $ \mu_{\rm TeVeS} $ at the 95% confidence level.
• The analysis shows that omitting range data from trajectory fitting increases residual variance, enabling better detection of potential gravitational anomalies.
• The study demonstrates that current Cassini data are sensitive enough to probe deviations from General Relativity at levels below the current PPN and fifth-force constraints.