A Cusp in the Symmetry Energy, PREX-II and Quasifermions in the Core of Massive Neutron Stars

The "dilemma" posed by the recent announcement of the PREX-II measurement of the neutron skin of $^{208}$Pb that suggests a stiff symmetry energy near nuclear matter density $n_0$ and its impact on the EoS of massive compact stars raise the issue as to whether the EoS determined at $n_0$ necessarily gives a stringent constraint at high densities relevant to massive compact stars, the currently widely accepted "lore" in astro-nuclear field. We present the argument that the "cusp" structure in the symmetry energy at $n_{1/2}\gtrsim 2 n_0$ predicted by a topology change in dense matter encoding hadron-quark continuity could provide a strong obstruction to the validity of the "lore." The topology change predicts an EoS that is soft below and stiffened above $n\gtrsim n_{1/2}$, involving no phase transitions, and yields the macrophysical properties of neutron stars more or less consistent with the overall observations and the maximum mass $ 2.0\lesssim M/ M_\odot\lesssim 2.2$ as well as the GW data. Furthermore it describes the interior core of the massive stars constituted of baryon-charge-fractionalized quasifermions, that are neither baryonic nor quarkonic, with the "pseudo-conformal" sound speed $v^2_{pcs}/c^2\approx 1/3$ with a nonzero trace of energy-momentum tensor converging from below at $n_{1/2}$.