It has been conjectured that, at sufficiently high baryon densities, the equation of state (EoS) of bulk nuclear matter can be identified with that of the nucleon core. In this work, we illustrate how the energy density and pressure distributions inside individual nucleons can be utilized to construct the EoS of supra-dense matter. In our framework, nucleons arise as topological solitons stabilized by vector mesons, which are dynamically generated through the path integral bosonization of an underlying Nambu-Jona-Lasinio (NJL) model. The restoration of chiral symmetry is implemented dynamically via a self-consistent, density-dependent scalar field, which modifies the (isovector) and (isoscalar) channels of the soliton. We analyze the resulting changes in soliton properties for different NJL parameter sets and demonstrate that the progressive restoration of chiral symmetry leads to a stiffening of the soliton-based EoS, making it compatible with existing neutron star EoSs. An EoS constructed from the solutions of the energy-density and pressure profiles at the center of the nucleon is also explored.
"the progressive restoration of chiral symmetry leads to a stiffening of the soliton-based EoS, making it compatible with existing neutron star EoSs" — i.e. when the in-medium scalar field S(s) is evolved self-consistently in the bosonized NJL soliton (with χ-renormalized energy density), the resulting p(ε) at s ~ 0.2–0.3 f_π reaches stiffness comparable to SLy4 / QHC18, in contrast to a naive (F*_π/f_π)^{2,4} rescaling which overestimates stiffening.
The identification of the mechanical pressure inside an isolated nucleon's hard core (a soliton in vacuum-like boundary conditions) with the thermodynamic pressure of bulk supra-saturation matter (Sec. 1, following Fukushima-Kojo-Weise [51]). Compounding this: (i) the ad hoc phenomenological scaling factor χ ≡ M_N^obs / M_slt^vac to substitute for spin–isospin quantization (Eq. 39), kept fixed at its vacuum value in-medium; (ii) freezing the scalar coupling g_s* to its s=0 value (Eq. 54) because the self-consistent gap equation has no solution beyond ~3 ρ_sat — an admitted breakdown of the framework precisely in the regime of interest.
1/ Idea: treat the nucleon as a topological soliton of pion + ω + ρ fields derived by path-integral bosonization of an NJL model. Inside the soliton there is a localized energy-density and pressure profile; reading p(ε) off that profile gives a candidate "nucleon EoS" for dense matter. 2/ New ingredient: chiral symmetry restoration is implemented self-consistently through a density-dependent scalar field S(s), which modifies F_π, M_π, M_v, g_v simultaneously. They show that a simple (F*_π/f_π)^n rescaling overestimates stiffening because it ignores the softening from M_v(s); the self-consistent treatment reaches NS-EoS-like stiffness at moderate s ~ 0.2–0.3 f_π once a vacuum-fit χ rescales the soliton mass to 939 MeV. 3/ Limits: no spin–isospin quantization (replaced by a single phenomenological χ), the in-medium gap equation breaks down past ~3 ρ_sat so g_s* is frozen to its vacuum value, surface vs central readouts give different EoSs, and the central physical assumption — that nucleon-core mechanical pressure equals bulk thermodynamic pressure — is conjectural. Hard-core overlap suggests deconfinement at 7–10 ρ_sat.
Imagine a proton as a tiny squishy ball. They squeeze many balls together to guess what neutron-star insides feel like.
This is a coherent extension of the Fukushima–Kojo–Weise "nucleon-core = bulk EoS" picture, replacing their qualitative F*_π rescaling by a self-consistent NJL bosonization where scalar and vector sectors are tied to one in-medium scalar field S. The numerics (relaxation method, Richardson extrapolation, benchmark against shooting and against [51]) appear competently done and the appendix error analysis is concrete. However, several load-bearing approximations are stacked: (i) the conjecture that mechanical pressure inside a static, unquantized soliton equals thermodynamic bulk pressure; (ii) a single multiplicative χ standing in for full spin–isospin quantization, applied uniformly to ε but inversely to p; (iii) freezing g_s* at its vacuum value because the fully self-consistent gap equation fails beyond ~3 ρ_sat — exactly the regime the paper claims to address; (iv) pseudo-gauge ambiguity in the EMT handled via a "pragmatic" mixed canonical/Belinfante prescription. The authors are explicit about most of these, which is to their credit, but the "compatibility with NS EoS" claim is sensitive to all of them, especially χ (Fig. 7a vs 7b shows χ controls stiffness). Novelty is incremental over [51] and over Chanfray et al.'s CCM line. Verdict: conditional — the model-building is fine, but the central phenomenological bridge to neutron-star matter rests on assumptions the paper itself flags as needing future work (confinement, quantization, β-equilibrium, Wigner–Seitz).