Constraining theories of gravity by GINGER experiment

The debate on gravity theories to extend or modify general relativity is very active today because of the issues related to ultraviolet and infrared behavior of Einstein’s theory. In the first case, we have to address the quantum gravity problem. In the latter, dark matter and dark energy, governing the large-scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of the art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here, we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar–tensor or Horava–Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense–Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe B satellites.

Results of space experiments and effect of torsion

The results of two space experiments, around the world clocks and gravity probe B, are analyzed theoretically using a field theory. The field equations of this theory are reduced to those of general relativity outside material distribution, while its equations of motion are not a geodesic one. This equation violates the weak equivalence principle because of the non-vanishing torsion in the geometry used. The predictions of the theory give rise to the time dilation measured by the first experiment and to the geodetic and frame drag effects measured by the second experiment. Furthermore, we show that these predictions are affected by the torsion of space-time. The torsion term, in the equation of motion, is connected to other effects through a coupling parameter. This parameter is called the “spin-torsion” coupling if the moving test particle is elementary one with non-vanishing quantum spin. We call this parameter “rotation-torsion” coupling if the moving test particle is a gyroscope. In the first case, the coupling parameter is well defined and confirmed by terrestrial experiment, while in the second case the parameter still needs further investigation and discussion.

Is There Still Something Left That Gravity Probe B Can Measure?

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment J 2 of its primary without any restriction on either the gyro’s orbital configuration and the orientation in space of the symmetry axis k ^ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin’s declination δ which may be as large as ≲30–40 milliarcseconds per year mas yr − 1 , depending on the initial orbital phase f 0 . Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector S and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin’s declination rate amounts to σ δ ˙ GP − B = 18.3 mas yr − 1 . We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary’s angular momentum J . In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.

Gravitomagnetism in modified theory of gravity

We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffat’s Modified theory of Gravity (MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the MOG gravitomagnetic field and that predicted by the Einstein’s gravitational theory and measured by Gravity Probe B, LAGEOS and LAGEOS 2, and with a number of GRACE and Laser Lunar ranging measurements requires [Formula: see text].