  In a recent work, it has been proposed that the recent cosmic passage to a
cosmic acceleration era is the result of the existence of small anti-gravity
sources in each galaxy and clusters of galaxies. In particular, a swiss-cheese
cosmology model which relativistically integrates the contribution of all these
anti-gravity sources on galactic scale has been constructed assuming the
presence of an infrared fixed point for a scale dependent cosmological
constant. The derived cosmological expansion provides explanation for both the
fine tuning and the coincidence problem. The present work relaxes the previous
assumption on the running of the cosmological constant and allows for a generic
scaling around the infrared fixed point. Our analysis reveals in order to
produce a cosmic evolution consistent with the best $\Lambda$CDM model, the
IR-running of the cosmological constant is consistent with the presence of an
IR-fixed point.
