The problem of two Hubble constants persistsThe 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 l_{H}= 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 manysheeted spacetime was one of the first applications of TGD inspired cosmology. The local value of Hubble constant would correspond to spacetime sheets of size at most that of large void. Global value would correspond to spacetime sheets with size scales up to ten billion years assignable to the entire observed cosmos. The smaller value of the Hubble constant for spacetime 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 manysheetedness. Reader has perhaps noticed that I have been talking about spacetime sheets in plural. The spacetime of TGD is indeed manysheeted 4D surface in 8D M^{4}×CP_{2}. It corresponds approximately to GRT spacetime 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 spacetime of GRT characterized by metric and gauge potentials in standard model. Manysheetedness leads to predictions allowing to distinguish between GRT and TGD. For instance, the propagation velocities of particles along different spacetime sheets can differ since the lightvelocity along spacetime sheets is typically smaller than the maximal signal velocity in empty Minkowski space M^{4}. 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 spacetime 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.
