Cosmic strings account for primordial SMBH production?

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This paper, http://arxiv.org/abs/1505.01584, Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe? offers a possible solution to the problem of SMBH abundances in the early universe at z~6. I suspended my abhorrence to the notion of cosmic strings to give this a look and it appears reasonable within the context of the authors' assumptions.
 
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This would have to be reconciled with the current non-detection of cosmic strings, both in their impact on the energy density of the early universe (cosmic strings have w = -1/3, which can markedly change a number of observational parameters for the early universe), and in terms of the failure of cosmological observations of strings at later times (primarily through gravitational lensing). It just seems unlikely that there can be enough cosmic strings around for such collisions to occur with any frequency.
 
It appears, to me, the authors adequately accounted for cosmic string abundance in their analysis.
 

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