Do cosmic strings with large string tension exist?

There is some empirical support for cosmic strings with a rather large string tension from gravitational lensing. Cosmic string tension T and string deficit angle Δ θ for lensing related bia the formula Δ θ = 8π× TG if general relativity is assumed to be a good description. The value of TGD deduced from data is TG= .05 and is very large and corresponds to an angle deficit Δ θ≈ 1.

For the ordinary value of Planck constant, TGD predicts the value of TG has upper bound in the range 10^-7-10^-6. The flat velocity spectrum for distant stars around galaxies determines the value of TG: one has v²=2TG from Kepler law so that the value of TG is determined from the measured value of the velocity v. The value of TG can be also deduced from the energy density of cosmic string-like objects predicted by TGD and is consistent with this estimate. If one takes the empirical evidence for a large value of TGseriously one must ask whether TGD can explain the claimed finding.

Could a large value of h_eff solve the discrepancy? String tension T as the linear energy density of the cosmic string is determined by the sum of Kähler action and volume term. The contribution of Kähler action to T is proportional to 1/α_K = g_K²/4πℏ. If cosmic string represents dark matter in TGD sense, one must make the replacement ℏ→ ℏ_eff so that the Kähhler contribution to T is proportional to ℏ_eff/ℏ. If the two contributions are of same order of magnitude or Kähler contribution dominates, ℏ_eff/ℏ=n≈ 10⁵ would give the needed large value TG. The physical interpretation would be that cosmic string is an n-sheeted structure with each sheet giving the same contribution so that the value of T is scaled up by n≈ 10⁵.

The physical interpretation would be that the cosmic string is an n-sheeted structure with each sheet giving the same contribution so that the value of T is scaled up by n≈ 10⁵. There are two options. The n-sheetedness is with respect to M⁴ so that one has a n-fold covering of M⁴ or with respect to CP₂ in which case one quantum coherent structure consisting of n parallel flux tubes.

It is intereting to consider in more detail the quantum model for the particles in the gravitational field of cosmic string.

1. The gravitational field of a straight cosmic string behaves like 1/ρ as a function of the radial distance ρ from string, and Kepler's law predicts a constant velocity v²= 2TG for circular orbits irrespective of their radius. This explains the flat velocity spectrum of stars rotating around galaxies.
2. Nottale proposed that planetary orbits obey Bohr quantization for the value of gravitational Planck constant ℏ_gr= GMm/β₀ assignable to a pair of masses M and M associated with the gravitational flux tube mediating the gravitational interaction between M and m.
3. If the mass M corresponds to a cosmic string idealized as straight string with an infinite length, the definition of ℏ_gr is problematic since M diverges. Therefore the application of Nottale's quantization to a distant star rotating cosmic string is problematic.

   What is however clear that ℏ_gr should be proportional to m by Equivalence Principle and one should have ℏ_gr= GM_effm/β₀ for the cosmic string. M_eff= TL_eff, where L_eff is the effective length of the cosmic string is also a reasonable parametrization.

4. Kepler law does not tell anything about the value of the radius r of the circular orbit. If the value of ℏ_gr is fixed somehow, one can apply the Bohr quantization condition ∮ pdq= nh_gr of angular momentum to circular orbits to obtain vr= nGM_eff giving

   r_n=nr₁,
   r₁=r_S,eff/[2(TG)^1/2β₀].

   A reasonable guess is that β₀ and the rotation velocity v/c=(2TG)^1/2 have the same order of magnitude. v/c= xβ₀< 1 would give β₀= (2TG)^<1/2/x. The minimal value of the orbital radius would be r₁=r_S,eff/[2xβ₀²].

See the chapter Magnetic Bubbles in TGD Universe: Part I or an article with the same title.