I can think of two TGD explanations for two different Hubble constants - this is how I see the problem - and it should be time to think this through again.

- The first TGD explanation coming into mind is based on many-sheeted space-time that I proposed decades ago. The Hubble constant depends on space-time sheet, in particular it depends on the p-adic scale assignable to the space-time sheet. Could the measured values of Hubble constant which differ by 9 per cent could correspond to different space-time sheets having slightly different Hubble constants. p-Adic length scales come as half octaves and different p-adic lengths scales would suggest a larger difference.

- Could length scale dependent of cosmological constant predicted by TGD (see solve the problem? Could it lead to length scale dependent Hubble constant H explaining the 9 per cent discrepancy as reflecting different values of H at long and short distances or equivalently at different values of cosmological time?

- TGD predicts length scale dependent cosmological constant and phase transitions inducing accelerated expansion (due to accelerated thickening of monopole flux tubes) as their magnetic energy transforms to ordinary matter (see this). Eventually the increase of volume energy stops his accelerated expansion. This fastens the expansion rate temporarily. Inflation and the recent accelerated expansion would be examples of this kind jerks replacing smooth cosmological expansion in TGD Universe. These jerks occur in all scale: even in scale of Earth (see this).

- The square H
^{2}of Hubble constant (see Friedmann equation ).

is sum of 3 contributions.

- The first term is proportional to mass density ρ
_{m}and given by

8π G ρ

_{m}/3,

where ρ

_{m}is the density of matter.

- Second "kinematic" contribution

-k/a

^{2}

depending on the parameter k=-1,0,1 characterizing the 3-curvature of 3-space. For hyperbolic cosmology expanding forever one has k=-1. Curvature radius a corresponds in TGD to the light-cone proper time coordinate.

- The third term given by

Λ/3

corresponds to cosmological constant. It is positive since the expansion is accelerated. This observation was fatal for superstring theory.

- The first term is proportional to mass density ρ
- What is new that in TGD Λ is (p-adic) length scale dependent and expected to come as negative powers of 2. Dark energy density is estimated to be 68 per cent of the total so that this term is the largest and the reduction of this term in the formula for H
^{2}by factor of say 1/4 is expected to have much larger effect on H^{2}than 9 per cent. The value of Λ must be same for the measurements giving different value of H as already noticed.

- Λ corresponds the sum of magnetic and volume energy densities defining the dark matter density having also interpretation as galactic dark matter. It is assignable to monopole flux tubes. Λ decreases during the accelerated period of expansion since magnetic energy decays to ordinary matter and increases the contribution of ρ
_{m}. These changes do not however cancel each other. The dark energy is transformed to matter during the acceleration period but the visible matter participates the expansion and its density is reduced during expansion. Hence the value of H^{2}should decrease.

- Could this give rise to a net effect so that the value of H
^{2}would change during the acceleraion period? Since the time of emission for the radiation depends on the distance of the object, the redshift of the radiation giving information about H at different stages of accelerated expansion. For long distances the net decrease of H should be larger and the measurements of H from large distances should give a smaller value of H.

This argument is rough but the key idea should be clear. The question is whether length scale dependent cosmological constant could solve the discrepancy? It turns out that the actual 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 this environment is younger than for nearby ones and the ageing of the flux tubes involving the decay of magnetic energy to ordinary matter would explain why the nearby flux tubes correspond to a larger value Hubble constant.

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