A TGD based resolution of the tension between neutrino mass scale deduced from neutrino mixing and from gravitational lensing

I learned about very interesting findings related to neutrinos (see this). The 3 neutrino families are known to mix and from various experiments, also from those performed in the laboratory, one can deduce estimates for the analog of the CKM matrix describing the mixing. This also allows us to estimate the sum of the neutrino masses.

One can also deduce information about neutrino masses from cosmology. The information comes from gravitational lensing. The gravitational lensing increases with so called clumpiness which measures how the inhomogeneities of mass density are. If one assumes standard cosmology with cold dark matter, one expects that the larger the average neutrino mass scale is, the larger the effects of the neutrino mass density on the clumpiness of the universe is.

According to the popular article, DESI maps out cosmic structures to determine the expansion rate through an effect known as baryon acoustic oscillations, sound waves that imprinted circular patterns on the very early universe. By tracing those patterns at different points in the universe s history, scientists can track its growth, kind of cosmic tree rings are in question.

Combining the measurements of clumpiness from the cosmic microwave background and the expansion rate from DESI two things that neutrinos affect makes it possible for scientists to deduce estimates for the sum of neutrino masses. The upper limit turned out to be unexpectedly small, about .07 eV. This is very near to the lower bound for the sum, about .06 eV deduced from the neutrino mixing. There are even experiments suggesting an upper limit of .05 eV in conflict with neutrino mixing data.

The outcome suggests that something goes wrong with the standard cosmology. Could it be that neutrinos do not affect the clumpiness so much as believed? Could neutrinos be lighter in the early cosmology? Or is the view of how clumpiness is determined, entirely wrong? Could the mechanism behind the gravitational lensing be something different from what it is believed to be?

This brings to mind what is called the clumpiness paradox about which I have written a blog posting (see this). Clumpiness paradox means that the clumpiness depends on the scale in which it is estimated. Clumpiness is smaller in long length scales. One proposal is that in long length scales clumpiness is determined to a high degree by the mass density of ultralight axions. The clumps have been now observed also in shorter scales. The strange conclusion is that cold dark matter is colder in short scales. One would expect just the opposite to be true.

The scale dependence of clumpiness suggests a fractal distribution of matter and dark matter. Indeed, in the TGD framework, cosmic strings thickened to monopole flux tubes forming scale hierarchy would be responsible for the gravitational lensing and the thickness of the monopole flux tubes would characterize the lensing. The explanation for the large size of the clumps in long scales would be the large size of the Compton length proportional to effective Planck constant h_eff=nh₀. In the case of gravitational Planck constant h_eff= h_gr= GMm/β₀, β₀ a velocity parameter, assignable to the monopole flux tubes connecting pairs formed by a large mass M and small mass m, the gravitational Compton length is equal to Λ_gr= GM/β₀= r_s/2β₀, r_s Schwartshild radius of M increasing with the size scale of structure (note that there is no dependence on m). The larger the scale of the studied astrophysical object, the larger Λ_gr as minimal gravitational quantum coherence length is, and the smaller the clumpiness in this scale.

This would predict the effect of neutrinos and also other particles on lumping and gravitational lensing is negligible. Cosmic strings would explain the lumping. The model would also explain why the upper bound for the sum of neutrino masses is inconsistent with the findings from neutrino mixing.

For the TGD view of cosmology see this, this, and this.

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.