Cusp in the Symmetry Energy, PREX-II And Pseudo-Conformal Sound Speed in Neutron Stars

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 widely accepted lore in nuclear astrophysics that the EoS determined at $n_0$ necessarily gives a stringent ``constraint at high densities relevant to massive compact stars. We present the argument that the ``cusp structure in the symmetry energy at $n_{1/2}gsim 2 n_0$ predicted by a topology change in dense matter could obstruct the validity of the lore. The topology change, encoding the emergence of QCD degrees of freedom in terms of hidden local and scale symmetries, predicts an EoS that is soft below and stiff above $ngsim n_{1/2}$, involving no low-order phase transitions, and yields the macrophysical properties of neutron stars overall consistent with the astrophysical observations including the maximum mass $ 2.0lsim M/ M_odotlsim 2.2$ as well as the GW data. Furthermore it describes the interior core of the massive stars constituted of baryon-charge-fractionalized quasi-fermions, that are neither baryonic nor quarkonic, with the ``pseudo-conformal sound speed $v^2_{pcs}/c^2approx 1/3$ converged from below at $n_{1/2}$ with a nonzero trace of energy-momentum tensor. { In the renormalization-group approach to interacting fermions dubbed $Gn$EFT, the strangeness degrees of freedom play no role in the density regime relevant to the massive stars considered.}