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The renormalization group (RG) approach to cosmology is an efficient methodto study the possible evolution of the cosmological parameters from the pointof view of quantum field theory in curved space-time. In this work we continueour previous investigations of the RG method based on potential low-energyeffects induced from physics at very high energy scales M_X near M_P. In thepresent instance we assume that both the Newton constant, G, and thecosmological term, \Lambda, can be functions of a scale parameter \mu. It turnsout that G(\mu) evolves according to a logarithmic law which may lead toasymptotic freedom of gravity, similar to the gauge coupling in QCD. At thesame time \Lambda(\mu) evolves quadratically with \mu. We study the consistencyand cosmological consequences of these laws when \mu=H. Furthermore, we proposeto extend this method to the astrophysical domain after identifying the localRG scale at the galactic level. It turns out that Kepler's third law ofcelestial mechanics receives quantum corrections that may help to explain theflat rotation curves of the galaxies without introducing the dark matterhypothesis. The origin of these effects (cosmological and astrophysical) couldbe linked, in our framework, to physics at M_X= 10^{16-17} GeV.Comment: LaTeX, 34 pages, 2 eps figures. Discussion enlarged, references  added. Final version accepted in JCA

RunningGand Λ at low energies from physics atMX: possible cosmological and astrophysical implications

RunningGand Λ at low energies from physics atM_X: possible cosmological and astrophysical implications