The main goal of this project is to investigate the phenomenological aspects of ERG approach to Quantum Gravity in the IR (astrophysical) scale. Thus, to test the presence of a non-trivial evolution of Λ(k) based on the RG trajectory, using various astrophysical and cosmological data. In a recent work we have proposed a solution of the cosmic acceleration and its coincidence problem without new energy scales or fine tuning. We have proposed that the recent cosmic acceleration can be the result of the existence of local antigravity sources (due to IR gravity corrections) associated with the existing astrophysical matter configurations (galaxies and clusters) distributed throughout the universe. The present project will try to further elaborate and improve this published work, using concrete ERG calculations and non homogeneous matching. SUBGOAL 1. Matching local astrophysical metrics with global cosmological metric. SUBGOAL 2. New non-singular spherical solutions