Solar System and stellar tests of a quantum-corrected gravity

The renormalization group running of the gravitational constant has a universal form and represents a possible extension of general relativity. These renormalization group effects on general relativity will cause the running of the gravitational constant, and there exists a scale of renormalization, which depends on the mass of an astronomical system and needs to be determined by observations. We test renormalization group effects on general relativity and obtain the upper bounds of in the low-mass scales: the Solar System and five systems of binary pulsars. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain new upper bounds on in the Solar System when the Lense--Thirring effect due to the Sun's angular momentum and the uncertainty of the Sun's quadrupole moment are properly taken into account. These two factors were absent in the previous work. We find that INPOP10a yields the upper bound as = (0. 32. 8) 10^-20 while EPM2011 gives = (-2. 58. 3) 10^-21. Both of them are tighter than the previous result by 4 orders of magnitude. Furthermore, based on the observational data sets of five systems of binary pulsars: PSR J0737-3039, PSR B1534+12, PSR J1756-2251, PSR B1913+16, and PSR B2127+11C, the upper bound is found as = (-2. 65. 1) 10^-17. From the bounds of this work at a low-mass scale and the ones at the mass scale of galaxies, we might catch an updated glimpse of the mass dependence of, and it is found that our improvement of the upper bounds in the Solar System can significantly change the possible pattern of the relation between log|| and logm from a linear one to a power law, where m is the mass of an astronomical system. This suggests that || needs to be suppressed more rapidly with the decrease of the mass of low-mass systems. It also predicts that || might have an upper limit in high-mass astrophysical systems, which can be tested in the future.