It is an undoubtedly grand challenge to unify gravity with the other fundamental interactions. One of the proposed routes is the concept of the non-commutative spectral geometry (NCSG), where the correction of the NCSG solution to Einstein’s general relativity in 4D spacetime can be characterized by a parameter β. This parameter contributes a Yukawa-type correction to the Newtonian gravitational potential at the leading order, which can be related to either the massive component of the gravitational field or the typical range of interactions carried by that component of the field. Therefore, measuring the lower bound on β can provide us a better understanding of the NCSG theory.

    In the recent investigation, the author extends the previous works to test the NCSG theory in the Solar System and stellar systems. Although the laboratory-scale experiments are better suited for the purpose, more estimates in the astronomical systems can improve statistics. Furthermore, more estimations obtained in systems with various scales can give a better idea on how the size of the system and accuracy of observations can (together) affect the estimate of the lower limit of β. The astronomical scale systems considered in this work yield the lower bounds on β on the order of 10⁻⁹–10⁻¹⁰ m⁻¹ (see Fig. 1), which are compatible with earlier results of a similar scale. Since the smaller-scale experiments can provide much stronger constraints on the lower limit of β, the laboratory-scale experiments (such as the torsion balance experiment) and especially the experiments in the high-energy particle physics are the most promising systems for testing predictions of the NCSG theory.

   This work is published by the journal of European Physical Journal Plus. And this research is supported by the National Nature Science Foundation of China under Grant Nos 11473072, 11533004 and 11103085.  For more details, please see the following link: https://link.springer.com/article/10.1140%2Fepjp%2Fi2017-11376-1