Preliminary bounds of the gravitational Local Position Invariance from Solar System planetary precessions

TL;DR

This paper derives bounds on the Whitehead parameter , testing gravitational Local Position Invariance using Solar System planetary precessions, and finds no evidence for deviations from General Relativity within current measurement limits.

Contribution

It provides the first bounds on  from planetary precession data and discusses how future missions could improve these constraints.

Findings

Bound on : ||  5.8 7

Ratio of perihelion precessions constrains  to zero

Current bounds are comparable to future mission sensitivities

Abstract

In the framework of the Parameterized Post-Newtonian (PPN) formalism, we calculate the long-term Preferred Location (PL) effects, proportional to the Whitehead parameter $\xi$, affecting all the Keplerian orbital elements of a localized two-body system, apart from the semimajor axis $a$. They violate the gravitational Local Position Invariance (LPI), fulfilled by General Relativity (GR). We obtain preliminary bounds on $\xi$ by using the latest results in the field of the Solar System planetary ephemerides. The non-detection of any anomalous perihelion precession for Mars allows us to indirectly infer $|\xi|\leq 5.8\times 10^{-6}$. \textcolor{black}{Such a bound is close to the constraint, of the order of $10^{-6}$, expected from the future BepiColombo mission to Mercury. As a complementary approach, the PL effects should be explicitly included in the dynamical models fitted to planetary data sets to estimate $\xi$ in a least-square fashion in a dedicated ephemerides orbit solution.} The ratio of the anomalous perihelion precessions for Venus and Jupiter, determined with the EPM2011 ephemerides at the $<3\sigma$ level, if confirmed as genuine physical effects needing explanation by future studies, rules out the hypothesis $\xi \neq 0$. A critical discussion of the $|\xi| \lesssim 10^{-6}-10^{-7}$ upper bounds obtained in the literature from the close alignment of the Sun's spin axis and the total angular momentum of the Solar System is presented.