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The Lunar Laser Ranging (LLR) experiment provides precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of highly accurate measurements of the distance between the Earth and Moon provide unique information that determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Analyses of precise laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-0.8 +/- 1.3) x 10^{-13} for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, (m_G/m_I)_E - (m_G/m_I)_M. Such an accurate result allows other tests of gravitational theories. Focusing on the tests of the EP, we discuss the existing data and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches to solutions. Additional high accuracy ranges and improvements in the LLR data analysis model will further advance the research of relativistic gravity in the solar system, and will continue to provide highly accurate tests of the Equivalence Principle.
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We study the impact of the limit on $|dot{G}|/G$ from Lunar Laser Ranging on nonlocal gravity, i.e. on models of the quantum effective action of gravity that include nonlocal terms relevant in the infrared, such as the RR and RT models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on the analysis of Barreira et al. [1] and we confirm their findings that (under plausible assumptions such as the absence of strong backreaction from non-linear structures), the RR model is ruled out. We also show that the mechanism of perfect screening for free suggested for the DW model actually does not work and the DW model is also ruled out. In contrast, the RT model passes all phenomenological consistency tests and is still a viable candidate.
We briefly summarize motivations for testing the weak equivalence principle and then review recent torsion-balance results that compare the differential accelerations of beryllium-aluminum and beryllium-titanium test body pairs with precisions at the part in $10^{13}$ level. We discuss some implications of these results for the gravitational properties of antimatter and dark matter, and speculate about the prospects for further improvements in experimental sensitivity.
We present new constraints on Lorentz symmetry (LS) violations with lunar laser ranging (LLR). Those constraints are derived in the standard-model extension (SME) framework aiming at parameterizing any LS deviations in all sectors of physics. We restrict ourself to two sectors namely the pure gravitational sector of the minimal SME and the gravity-matter coupling. We describe the adopted method and compare our results to previous analysis based on theoretical grounds. This work constitutes the first direct experimental determination of the SME coefficients using LLR measurements.
General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on one of the most fundamental principles of Nature, the Equivalence Principle, which represents the core of the Einstein theory of gravity. The confirmation of its validity at different scales and in different contexts represents one of the main challenges of modern physics both from the theoretical and the experimental points of view. A major issue related to this principle is the fact that we actually do not know if it is valid at quantum level. Furthermore, recent progress on relativistic theories of gravity have to take into account new issues like Dark Matter and Dark Energy, as well as the validity of fundamental principles like local Lorentz and position invariance. Experiments allow to set stringent constraints on well established symmetry laws, on the physics beyond the Standard Model of particles and interactions, and on General Relativity and its possible extensions. In this review, we discuss precision tests of gravity in General Relativity and alternative theories and their relation with the Equivalence Principle. In the first part, we discuss the Einstein Equivalence Principle according to its weak and strong formulation. We recall some basic topics of General Relativity and the necessity of its extension. Some models of modified gravity are presented in some details. The second part of the paper is devoted to the experimental tests of the Equivalence Principle in its weak formulation. We present the results and methods used in high-precision experiments, and discuss the potential and prospects for future experimental tests.
The possibility for Lorentz/CPT-breaking, which is motivated by unification theories, can be systematically tested within the standard-model extension framework. In the pure gravity sector, the mass dimension 5 operators produce new Lorentz and CPT-breaking terms in the 2-body equations of motion that depend on the relative velocity of the bodies. In this Letter, we report new constraints on 15 independent SME coefficients for Lorentz/CPT-violations with mass dimension 5 using lunar laser ranging. We perform a global analysis of lunar ranging data within the SME framework using more than 26,000 normal points between 1969 and 2018. We also perform a jackknife analysis in order to provide realistic estimates of the systematic uncertainties. No deviation from Lorentz/CPT symmetries is reported. In addition, when fitting simultaneously for the 15 canonical SME coefficients for Lorentz/CPT-violations, we improve up to three orders of magnitude previous post-fit constraints from radio pulsars.
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