A Local Lorentz Invariance test with LAGEOS satellites

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 $\alpha_1$, a parameter that has a null value in General Relativity. We constrain this parameterized post-Newtonian parameter down to the level of $\alpha_1 \le 2\times10^{-5}$, improving a previous limit obtained through the Lunar Laser Ranging technique.