Tests of Gravity Using Lunar Laser Ranging

A way forward for fundamental physics in space

Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Varying Physical Constants, Astrometric Anomalies, Redshift and Hubble Units

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.

Modeling and compensation of cross-axis coupling in an electrostatic accelerometer for testing the equivalence principle

Electrostatic accelerometers have extremely high sensitivity and are ideal scientific instruments for measuring very weak acceleration. In particular, a single-sensitive-axis electrostatic accelerometer can be used for testing the equivalence principle in space. Sensitive-axis capacitances formed by axial electrodes and a cylindrical proof mass vary with the axial motion of the mass and are also affected by radial motion, which results in cross-axis coupling disturbances. A quantitative model is built to analyze the cross-axis coupling effect on the sensitive axis from the radial suspension loop, including a nonlinear model for large radial motion and a linear model for small radial motion. Frequency response simulation shows that the cross-axis coupling effect for a small signal case arises mostly in the high-frequency range. Experiments are carried out with a ground-based electrostatic accelerometer made of a single, non-rotating test cylinder, and in this case, the experimental results are utilized to verify the mathematical model. Cross-axis coupling for small signal perturbations is virtually removed if the equilibrium position of the proof mass is calibrated to the null position of the sensor cage. In addition, data post-processing can further attenuate the cross-axis coupling disturbances when dealing with large radial motion. The cross-axis coupling disturbances on both the position and the acceleration measurement signals in the sensitive axis are mostly removed in ground-based experiments. The proposed model and compensation can be extended to space equivalence principle instruments and other electrostatic accelerometers with a cylindrical proof mass.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Next-generation hollow retroreflectors for lunar laser ranging

The three retroreflector arrays put on the Moon 40 years ago by the Apollo astronauts and the French-built arrays on the Soviet Lunokhod rovers continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant, as well as valuable insight into the Moon's interior. However, the precision of the ranging measurements are now being limited by the physical size of the arrays and a new generation of retroreflectors is required to make significant advances over current capabilities. Large single-cube retroreflectors represent the most promising approach to overcoming current limitations, and hollow retroreflectors in particular have the potential to maintain their good optical performance over the nearly 300 K temperature swing that occurs during the lunar cycle. Typically, epoxies are used for aligning and bonding hollow retroreflectors, but their thermal stability will predominantly be limited by the difference of the coefficient of thermal expansion (CTE) between the epoxy and the glass. A relatively new bonding method known as hydroxide catalysis bonding (HCB) has been used to adhere complex optical components for space-based missions. HCB has an extremely thin bond, a low CTE, and a high breaking strength that makes it an ideal candidate for bonding hollow retroreflectors for lunar laser ranging (LLR). In this work, we present results of a feasibility study of bonded Pyrex and fused silica hollow retroreflectors using both epoxy and HCB methods, including the results of thermally cycling the hollow retroreflectors from 295 to 185 K. Finally, we discuss the potential for using these retroreflectors for future LLR.

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10-5 - 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.