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It is argued that a well measured double neutron star binary in which the two neutron stars are more than 4% different from each other in mass or a massive neutron star with mass M > 2 M_sun would put in serious doubt or simply falsify the following chain of predictions: (1) nearly vanishing vector meson mass at chiral restoration, (2) kaon condensation at a density n ~ 3 n_0, (3) the Brown-Bethe maximum neutron star mass M_max ~ 1.5 M_sun and (4) Smolin's `Cosmological Natural Selection' hypothesis.
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See, e.g., the debate between L. Smolin and L. Susskind, in http://www.edge.org/3rd_culture/ smolin_susskind04/smolin_susskind.html
Cited in the paper.
A possible obstacle to this scenario is the appearance of negatively charged hyperons, e.g., Σ − \Sigma^{-} in the matter at a lower density. How this obstacle can be avoided in delayed collapse as well as loop-holes in the stadard arguments leading to this obstacle are discussed in [ 4 ]
Cited in the paper.
A star with condensed kaons might exhibit anomalous cooling as discussed in the literature. However this would require calculating the equation of state nonperturbatively in hidden local symmetry theory
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