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About the problem of two Hubble constants

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The usual formulation of the problem of two Hubble constants is that the value of the Hubble constant seems to be increasing with time. There is no convincing explanation for this. But is this the correct way to formulate the problem? In the TGD framework one can start from the following ideas discussed already earlier (see this).

  1. Would it be better to say that the measurements in short scales give slightly larger results for H0 than those in long scales? Scale does not appear as a fundamental notion neither in general relativity nor in the standard model. The notion of fractal relies on the notion but has not found the way to fundamental physics. Suppose that the notion of scale is accepted: could one say that Hubble constant does not change with time but is length scale dependent. The number theoretic vision of TGD brings brings in two length scale hierarchies: p-adic length scales Lp and dark length scale hierarchies Lp(dark)=nLp, where one has heff=nh0 of effective Planck constants with n defining the dimension of an extension of rationals. These hierarchies are closely related since p corresponds to a ramified prime (most naturally the largest one) for a polynomial defining an extension with dimension n.
  2. I have already earlier considered the possibility that the measurements in our local neighborhood (short scales) give rise to a slightly larger Hubble constant? Is our galactic environment somehow special?

Consider first the length scale hierarchies.

  1. The geometric view of TGD replaces Einsteinian space-times with 4-surfaces in H=M4times CP2. Space-time decomposes to space-time sheets and closed monopole flux tubes connecting distant regions and radiation arrives along these. The radiation would arrive from distant regions along long closed monopole flux tubes, whose length scale is LH. They have thickness d and length LH. d is the geometric mean d=(lPLH)1/2 of Planck length LP and length LH. d is of about 10-4 meters and size scale of a large neuron. It is somewhat surprising that biology and cosmology seem to meet each other.
  2. The number theoretic view of TGD is dual to the geometric view and predicts a hierarchy of primary p-adic length scales Lp ∝ p1/2 and secondary p-adic length scales L2,p =p1/2Lp. p-Adic length scale hypothesis states that p-adic length scales Lp correspond to primes near the power of 2: p ≈ 2k. p-adic primes p correspond to so-called ramified primes for a polynomial defining some extension of rationals via its roots.

    One can also identify dark p-adic length scales

    Lp(dark) =nLp ,

    where n=heff/h0 corresponds to a dimension of extension of rationals serving as a measure for evolutionary level. heff labels the phases of ordinary matter behaving like dark matter explain the missing baryonic matter (galactic dark matter corresponds to the dark energy assignable to monopole flux tubes).

  3. p-Adic length scales would characterize the size scales of the space-time sheets. The Hubble constant H0 has dimensions of the inverse of length so that the inverse of the Hubble constant LH∝ 1/H0 characterizes the size of the horizon as a cosmic scale. One can define entire hierarchy of analogs of LH assignable to space-time sheets of various sizes but this does not solve the problem since one has H0 ∝ 1/Lp and varies very fast with the p-adic scale coming as a power of 2 if p-adic length scale hypothesis is assumed. Something else is involved.

One can also try to understand also the possible local variation of H0 by starting from the TGD analog of inflation theory. In inflation theory temperature fluctuations of CMB are essential.

  1. The average value of heff is eff>=h but there are fluctuations of heff and quantum biology relies on very large but very rare fluctuations of heff. Fluctuations are local and one has p(dark)> = eff/h0> Lp. This average value can vary. In particular, this is the case for the p-adic length scale Lp,2 (Lp,2(dark)=nL2,p), which defining Hubble length LH and H0 for the first (second) option.
  2. Critical mass density is given by 3H02/8πG. The critical mass density is slightly larger in the local environment or in short scales. As already found, for the first option the fluctuations of the critical mass density are proportional to δ n/n and for the second option to -δ n/n. For the first (second) option the experimentally determined Hubble constant increases when n increases (decreases). The typical fluctuation would be δ heff/h ∼ 10-5. What is remarkable is that it is correctly predicted if the integer n decomposes to a product n1=n2 of nearly identical or identical integers.

    For the first option, the fluctuation δ heff/heff=δn/n in our local environment would be positive and considerably larger than on the average, of order 10-2 rather than 10-5. heff measures the number theoretic evolutionary level of the system, which suggests that the larger value of eff> could reflect the higher evolutionary level of our local environment. For the second option the variation would correspond to δn/n≤ 0 implying lower level of evolution and does not look flattering from the human perspective. Does this allow us to say that this option is implausible?

    The fluctuation of heff around h would mean that the quantum mechanical energy scales of various systems determined by eff>=h vary slightly in cosmological scales. Could the reduction of the energy scales due to smaller value of heff for systems at very long distance be distinguished from the reduction caused by the redshift. Since the transition energies depend on powers of Planck constant in a state dependent manner, the redshifts for the same cosmic distance would be apparently different. Could this be tested? Could the variation of heff be visible in the transition energies associated with the cold spot?

  3. The large fluctuation in the local neighbourhood also implies a large fluctuation of the temperature of the cosmic microwave background: one should have δT/T ≈ δn/n≈ δ H0/H0. Could one test this proposal?

See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.


Source: http://matpitka.blogspot.com/2024/03/about-problem-of-two-hubble-constants.html


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