Solution of Hubble constant discrepancy from the length scale dependence of cosmological constant

The discrepancy of the two determinations of Hubble constant has led to a suggestion that new physics might be involved (see this).

  1. Planck observatory deduces Hubble constant H giving the expansion rate of the Universe from CMB data something like 360,000 y after Big Bang, that is from the properties of the cosmos in long length scales. Riess's team deduces H from data in short length scales by starting from galactic length scale and identifies standard candles (Cepheid variables), and uses these to deduce a distance ladder, and deduces the recent value of H(t) from the redshifts.
  2. The result from short length scales is 73.5 km/s/Mpc and from long scales 67.0 km/s/Mpc deduced from CMB data. In short length scales the Universe appears to expand faster. These results differ too much from each other. Note that the ratio of the values is about 1.1. There is only 10 percent discrepancy but this leads to conjecture about new physics: cosmology has become rather precise science!
TGD could provide this new physics. I have already earlier considered this problem but have not found really satisfactory understanding. The following represents a new attempt in this respect.
  1. The notions of length scale are fractality are central in TGD inspired cosmology. Many-sheeted space-time forces to consider space-time always in some length scale and p-adic length scale defined the length scale hierarchy closely related to the hierarchy of Planck constants heff/h0=n related to dark matter in TGD sense. The parameters such as Hubble constant depend on length scale and its value differ because the measurements are carried out in different length scales.
  2. The new physics should relate to some deep problem of the recent day cosmology. Cosmological constant Λ certainly fits the bill. By theoretical arguments Λ should be huge making even impossible to speak about recent day cosmology. In the recent day cosmology Λ is incredibly small.
  3. TGD predicts a hierarchy of space-time sheets characterized by p-adic length scales (Lk) so that cosmological constant Λ depends on p-adic length scale L(k) as Λ∝ 1/GL(k)2, where p ≈ 2k is p-adic prime characterizing the size scale of the space-time sheet defining the sub-cosmology. p-Adic length scale evolution of Universe involve as sequence of phase transitions increasing the value of L(k). Long scales L(k) correspond to much smaller value of Λ.
  4. The vacuum energy contribution to mass density proportional to Λ goes like 1/L2(k) being roughly 1/a2, where a is the light-cone proper time defining the "radius" a=R(t) of the Universe in the Robertson-Walker metric ds2=dt2-R2(t) dΩ2. As a consequence, at long length scales the contribution of Λ to the mass density decreases rather rapidly.

    Must however compare this contribution to the density ρ of ordinary matter. During radiation dominated phase it goes like 1/a4 from T∝ 1/a and form small values of a radiation dominates over vacuum energy. During matter dominated phase one has ρ∝ 1/a3 and also now matter dominates. During predicted cosmic string dominated asymptotic phase one has ρ∝ 1/a2 and vacuum energy density gives a contribution which is due to Kähler magnetic energy and could be comparable and even larger than the dark energy due to the volume term in action.

  5. The mass density is sum ρmd of the densities of matter and dark energy. One has ρm∝ H2. Λ∝ 1/L2(k) implies that the contribution of dark energy in long length scales is considerably smaller than in the recent cosmology. In the Planck determination of H it is however assumed that cosmological constant is indeed constant. The value of H in long length scales is under-estimated so that also the standard model extrapolation from long to short length scales gives too low value of H. This is what the discrepancy of determinations of H performed in two different length scales indeed demonstrate.
A couple of remarks are in order.
  1. The twistor lift of TGD suggests an alternative parameterization of vacuum energy density as ρvac= 1/L4(k1). k1 is roughly square root of k. This gives rise to a pair of short and long p-adic length scales. The order of magnitude for 1/L(k1) is roughly the same as that of CMB temperature T: 1/L(k1)∼ T. Clearly, the parameters 1/T and R correspond to a pair of p-adic length scales. The fraction of dark energy density becomes smaller during the cosmic evolution identified as length scale evolution with largest scales corresponding to earliest times. During matter dominated era the mass density going like 1/a3 would to dominate over dark energy for small enough values of a. The asymptotic cosmology should be cosmic string dominated predicting 1/GT2(k). This does not lead to contradiction since Kähler magnetic contribution rather than that due to cosmological constant dominates.
  2. There are two kinds of cosmic strings: for the other type only volume action is non-vanishing and for the second type both Kähler and volume action are non-vanishing but the contribution of the volume action decreases as function of the length scale.
See the chapter More about TGD inspired cosmology or the article New insights about quantum criticality for twistor lift inspired by analogy with ordinary criticality .