A Local Lorentz Invariance test with LAGEOS satellites

TL;DR

This work probes Local Lorentz Invariance in gravity by constraining the PPN parameter $\alpha_1$ through long-term precise tracking of the LAGEOS and LAGEOS II satellites. The authors develop a two-satellite, phase-sensitive detection approach that isolates an annual modulation in the observable $\dot{\ell}_0 = \dot{\omega} + \dot{M}$, while cancelling dominant Earth's quadrupole errors via a linear combination of the two orbits. Two independent POD pipelines (GEODYN II and SATAN) analyzed roughly three decades of data, yielding consistent constraints: $\alpha_1 = (+2 \pm 3)\times 10^{-5}$ (GEODYN II) and $\alpha_1 = (+1 \pm 2)\times 10^{-5}$ (SATAN), with a 95% confidence upper limit of $|\alpha_1| < (4$–$6)\times 10^{-5}$. Translating this bound into the SME and Einstein‑aether contexts, the results impose tight restrictions on Lorentz-violating couplings in the gravitational sector, notably translating to $\bar{s}^{TT} \lesssim (4$–$6)\times 10^{-6}$. The analysis demonstrates a robust, direct Earth-orbit test of LLI in gravity and points toward extending the method to the eccentricity vector to constrain multiple PPN parameters simultaneously.

Abstract

Strong theoretical arguments suggest that a breakdown of Lorentz Invariance could arise under some very particular conditions. From an experimental point of view, it is important to test the Local Lorentz Invariance with ever greater precision and in all contexts, regardless of the theoretical motivation for the possible violation. In this paper we discuss some aspects of the gravitational sector. Tests of Lorentz Invariance in the context of gravity are difficult and rare in the literature. Possible violations could arise from quantum physics applied to gravity or the presence of vector and tensor fields mediating the gravitational interaction together with the metric tensor of General Relativity. We present our results in the latter case. We analyzed the orbit of the LAGEOS and LAGEOS II satellites over a period of almost three decades. The effects of the possible preferred frame represented by the cosmic microwave background radiation on the mean argument of latitude of the satellites orbit were considered. These effects would manifest themselves mainly through the post-Newtonian parameter $α_1$, a parameter that has a null value in General Relativity. We constrain this parameterized post-Newtonian parameter down to the level of $α_1 \le 2\times10^{-5}$, improving a previous limit obtained through the Lunar Laser Ranging technique.

Figures (30)

• Figure 1: GEODYN II analysis: LAGEOS (top) and LAGEOS II (bottom) 7-day residuals in the rate of the argument of pericenter (red) and in the rate of the mean anomaly (blue) as a function of time.
• Figure 2: GEODYN II analysis: LAGEOS and LAGEOS II residuals in the rate of the longitude ${\ell}_0={\omega}+{M}$ versus time. Note the different scale along the vertical axis with respect to Figure \ref{['fig:residui1']}.
• Figure 3: LAGEOS (top) and LAGEOS II (bottom) 7-day residuals in the rate of the argument of pericenter (red) and in the rate of the mean anomaly (blue) as a function of time from the analysis performed with SATAN.
• Figure 4: LAGEOS 7-day residuals in the rate of the mean argument of latitude (blue) obtained from the GEODYN II analysis compared with the same residuals obtained from the analyis performed with SATAN (red).
• Figure 5: GEODYN II (top) and SATAN (bottom). Time behavior for the variable $A_1(t)$ from the solutions of the system shown in Eq. (\ref{['equ_comb']}).