Testing Lorentz Symmetry with Lunar Laser Ranging

Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both general relativity and the standard model of particle physics called the standard-model extension (SME). We present new constraints on pure gravity SME coefficients obtained by analyzing lunar laser ranging (LLR) observations. We use a new numerical lunar ephemeris computed in the SME framework and we perform a LLR data analysis using a set of 20 721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR data are sensitive and not the same as those fitted in previous postfit residuals analysis using LLR observations and based on theoretical grounds. We found no evidence for Lorentz violation at the level of ${10}^{-8}$ for ${\overline{s}}^{TX}$, ${10}^{-12}$ for ${\overline{s}}^{XY}$ and ${\overline{s}}^{XZ}$, ${10}^{-11}$ for ${\overline{s}}^{XX}-{\overline{s}}^{YY}$ and ${\overline{s}}^{XX}+{\overline{s}}^{YY}-2{\overline{s}}^{ZZ}-4.5{\overline{s}}^{YZ}$, and ${10}^{-9}$ for ${\overline{s}}^{TY}+0.43{\overline{s}}^{TZ}$. We improve previous constraints on SME coefficient by a factor up to 5 and 800 compared to postfit residuals analysis of respectively binary pulsars and LLR observations.

Figure 1

Top: estimations of ${\overline{s}}^{XY}$ and ${\overline{s}}^A$ as a function of data subsamples by LLR stations. Each station name along the $x$ axis corresponds to the subsample without data from the corresponding station. Bottom: estimations of ${\overline{s}}^{XZ}$ and ${\overline{s}}^D$ as a function of data subsamples by lunar reflectors. L1 and L2 correspond to subsamples without respectively Lunokhod 1 and 2 data, while XI, XIV, and XV refer to subsamples without respectively Apollo XI, XIV, and XV data. The top and bottom error bars are those provided by the chi-square fit at $1{\sigma }_{\mathrm{stat}}$ standard deviation and the red line corresponds to the theoretical values of the SME coefficients in the GR framework.