We show that the cusplike structure in the nuclear symmetry energy, a consequence of topology change, visible in the skyrmion lattice description of dense matter, is extremely robust. It is present in the Skyrme model—with the pion field only—and is left unscathed by massive degrees of freedom such as the vector mesons $\rho$ and $\omega$ and also the scalar meson introduced as a dilaton. It leads to the emergence of parity-doubling at the skyrmion–half-skyrmion transition and impacts on the nuclear symmetry energy “wilderness” landscape, weeding out roughly half of the wilderness. It is shown that a pseudoconformal sound velocity arises at a precocious density at which the cusp is formed. It is suggested that the topology change, being robust, could impact on the tidal deformability observed in gravity waves

• Received 7 January 2019

DOI:https://doi.org/10.1103/PhysRevC.99.055808