Clumpiness paradox of cold dark matter scenario from the TGD point of view

Clumpiness paradox is one of the many problems plaguing the cold dark matter scenario (see this).

Clumpiness parameter (see this) is in principle deducible from the weak gravitational lensing caused by dark matter. In halo models it affects the annihilation rate of dark matter particles. Since the predicted rate is proportional to mass density squared, the annihilation rate increases for clumpy mass distribution.

If I understand correctly, the clumpiness paradox states that the clumpiness, which is determined by the size of dark matter clumps, depends on the scale in which observations are carried out. Clumpiness is smaller in long length scales, which means that the observed clumps are larger in long scales. In long scales, corresponding to recent cosmology, the sizes of clumps assignable are larger and the clumpiness parameter is .83. In shorter length scales corresponding to the age of the Universe about 380 thousand years the clumpiness parameter is smaller: .76.

In long length scales, a proposed explanation for the small value of clumpiness, i.e. a large size of clumps, is in terms of identification of dark matter as ultralight axions with very large Compton length determining the size scale of clumps.

This does not explain why the clumpiness depends on scale. Furthermore, clumps have been now observed in considerably smaller scales than earlier (see this). The strange looking conclusion is that cold dark matter is colder in short scales: the naive expectation would be just the opposite since it is the hot dark matter particles, which should form only small clumps. Something seems to go wrong.

The clumpiness paradox suggests a fractal distribution of dark matter. Indeed, in the TGD framework, cosmic strings thickened to monopole flux tubes would be responsible for 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.

See the articles Magnetic Bubbles in TGD Universe: Part I, Magnetic Bubbles in TGD Universe: Part II and TGD view of the paradoxical findings of the James Webb telescope.

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