I have considered the problem of two value of cosmological constant already earlier in the framework provided by many-sheeted space-time. In the sequel the puzzle of two Hubble constants is discussed applying the recent view about cosmological constant. What is new that twistor lift of TGD predicts that cosmological constant is length scale dependent and that cosmological expansion consists of jerkes involving accelerated periods followed by a phase transition changing reducing cosmological constant by a negative power of two and and inducing the transformation of the magnetic energy of monopole flux tubes to ordinary matter.
Monopole flux tubes have become a central element of TGD inspired cosmomology and astrophysics and the natural question is whether length scale dependent cosmological constant could solve the Hubble discrepancy? It seems that the higher value of cosmological constant corresponds to a smaller scale for observations: this could explain the discrepancy. The model requires a more detailed consideration of what it it is to be a standard candle. In many-sheeted space-time of TGD also the environment of the standard candle identified as monopole flux tube matters.
For distant standard candles the environment defined by the flux tube is younger than for nearby ones. The thickening associated with the ageing of the flux tubes involving the decay of magnetic energy to ordinary matter. The reduction of magnetic energy density in turn increases the value of the metric component gaaa)1/2 in the natural space-time coordinates provided by the Robertson-Walker coordinates of the light-cone (a corresponds to the proper time coordinate of the light-cone). This can give rise to the increase of the Hubble constant H= 1/(gaaa)1/2 explaining why the nearby flux tubes correspond to a larger value Hubble constant. Therefore monopole magnetic flux tubes could explain also the Hubble constant discrepancy.
For a summary of earlier postings see Latest progress in TGD.