Observational tests of the self-dual spacetime in loop quantum gravity

The self-dual spacetime was derived from the mini-superspace approach, based on the polymerization quantization procedure in loop quantum gravity (LQG). Its deviation from the Schwarzschild spacetime is characterized by the polymeric function $P$, purely due to the geometric quantum effects from LQG. In this paper, we consider the observational constraints imposed on $P$ by using the solar system experiments and observations. For this purpose, we calculate in detail the effects of $P$ on astronomical observations conducted in the Solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, and geodetic precession. The observational constraints are derived by confronting the theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the measurement of the gravitational time delay by the Cassini mission, which yields $0<P<5.5\times 10^{-6}$. In addition, we also discuss the potential constraint that can be obtained in the near future by the joint European-Japanese BepiColombo project and show that it could significantly improve the current constraints.