- The measurement of Hubble constant requires determination of distance of astrophysical object. For instance, the distance using so called standard candles - type I a supernovae having always same brightness decreasing like inverse square of distance (cosmic redshift also reduces the total intensity by shifting the frequencies). This method works for not too large distances (few hunder million light years, the size scale of the large voids): therefore this method gives the value of the local Hubble constant.
- The rate can be also deduced from cosmic redhift for CMB radiation. This method gives the Hubble constant in cosmic scales considerably longer than the size of large voids: one speaks of global determination of Hubble constant.
The explanation of the discrepancy in terms of many-sheeted space-time was one of the first applications of TGD inspired cosmology. The local value of Hubble constant would correspond to space-time sheets of size at most that of large void. Global value would correspond to space-time sheets with size scales up to ten billion years assignable to the entire observed cosmos. The smaller value of the Hubble constant for space-time sheets of cosmic size would reflect the fact that the metric for them corresponds to a smaller average density for them. Mass density would be fractal in accordance with the fractality of TGD Universe implied by many-sheetedness.
Reader has perhaps noticed that I have been talking about space-time sheets in plural. The space-time of TGD is indeed many-sheeted 4-D surface in 8-D M4×CP2. It corresponds approximately to GRT space-time in the sense that the gauge potentials and gravitational fields (deviation of induced metric from Minkowksi metric) for sheets sum up to the gauge potential and gravitational field for the space-time of GRT characterized by metric and gauge potentials in standard model. Many-sheetedness leads to predictions allowing to distinguish between GRT and TGD. For instance, the propagation velocities of particles along different space-time sheets can differ since the light-velocity along space-time sheets is typically smaller than the maximal signal velocity in empty Minkowski space M4. Evidence for this effect was observed for the first time for supernova 1987A: neutrinos arrived in two bursts and also gamma ray burst arrived at different time than neutrinos: as if the propagation would have taken place along different space-time sheets (see this). Evidence for this effect has been observed also for neutrinos arrived from galactic blackhole Sagittarius A. Two pulses were detected and the difference for arrival time was few hours (see this).
For details see the chapter More about TGD cosmology of "Physics in Many-Sheeted Space-time".
For a summary of earlier postings see Latest progress in TGD.