The rate of cosmic expansion manifesting itself as cosmic redshift is proportional to the distance r of the object: the expansion velocity satisfies v=Hr. The proportionality coefficients H is known as Hubble constant. Hubble constant has dimensions of 1/s. A more convenient parameter is Hubble length defined as lH= c/H, whose nominal value is 14.4 light years and corresponds to the limit at which the distant object recedes with light velocity from observer.
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 or the article Three astrophysical and cosmological findings from TGD point of view.