Solar System and stellar tests of noncommutative spectral geometry

Abstract

By using purely geometric forces on a noncommutative spacetime, noncommutative spectral geometry (NCSG) was proposed as a possible way to unify gravitation with the other known fundamental forces. The correction of the NCSG solution to Einstein's general relativity (GR) in the four-dimensional spacetime can be characterized by a parameter \(\beta\sim 1/\sqrt{f_{0}}\), where \( f_{0}\) denotes the coupling constants at the unification. The parameter \( \beta\) contributes a Yukawa-type correction \(\mathrm{exp}(-\beta r)/r\) to the Newtonian gravitational potential at the leading order, which can be interpreted as either the massive component of the gravitational field or the typical range of interactions carried by that component of the field. As an extension of previous works, we mainly focus on the Solar System and stellar tests of the theory, and the constraints on \(\beta\) obtained by the present work is independent of the previous ones. In the Solar System, we investigate the effects of the NCSG on the perihelion shift of a planet, deflection of light, time delay at superior conjunction (SC) and inferior conjunction (IC), and the Cassini experiment by modeling new observational results and adopting new datasets. In the binary pulsars system, based on the observational data sets of four systems of binary pulsars, PSR B1913+16, PSR B1534+12, PSR J0737-3039, and PSR B2127+11C, the secular periastron precessions are used to constrain this theory. These effects in the scale of the Solar System and binary pulsars were not considered in previous works. We find that the lower bounds given by these experiments are \(\beta \simeq 10^{-9} \sim 10^{-10}\) m-1, considerably smaller than those obtained in laboratory experiments. This confirms that experiments and observations at smaller scales are more favorable for testing the NCSG theory.