Tachyon-Free Forced Scalarization of Neutron Stars with a Non-Zero Vacuum

To eliminate at the effective field theory (EFT) level the linear tachyonic instability underlying spontaneous scalarization in conventional scalar-tensor theories (STT), we construct and numerically test a class of massive scalar-tensor models featuring a non-zero vacuum state and a spontaneous symmetry breaking (SSB) quartic barrier. Motivated by the self-consistency requirements of weak-field point-particle local rest-energy modulation and the weak equivalence principle, the dimensionless scalar vacuum state is anchored at $\phi_0=1$ (corresponding to the special-relativistic specific-energy scale $\Phi_0=c^2$). Protected by an ultraviolet $\mathbb{Z}_2$ symmetry, a negative non-minimal coupling ($\xi<0$), and a mesoscopic mass window, the perturbative effective mass squared remains strictly positive ($m_{\mathrm{eff}}^2>0$) throughout the full density domain of compact stars, converting scalar excitation into a tachyon-free ``forced scalarization'' driven directly by the trace of the matter energy-momentum tensor. To eliminate higher-order derivative couplings and low-density envelope truncation errors, we employ the contracted trace identity of the field equations to analytically remove the second-order metric derivative, explicitly decoupling the hydrostatic and even-parity tidal perturbation systems. Adopting a seven-segment continuous piecewise-polytropic equation of state (EOS) stitched with a four-layer BPS low-pressure crust, we perform 900 sets of $(\lambda,\xi)$ two-parameter grid shooting integrations for three nuclear EOSs (MPA1, SLy, and APR4) from the stellar center to the iron surface ($P_{\mathrm{surf}}=10^{-16}\,\mathrm{km}^{-2}$). The results demonstrate that mesoscopic heavy-mass Yukawa suppression matched to the microscopic quantum chromodynamics (QCD) scale ($\Lambda_p\approx 230\,\mathrm{MeV}$) and energy-momentum trace reversal ($\epsilon-3P\to 0$) in the ultra-relativistic core trigger a strong cooperative quenching, confining the scalar field within an extremely narrow algebraic potential well and exhibiting quasi-static saturation with respect to the self-coupling constant $\lambda$. Under the multimessenger-compatible MPA1 EOS, the total formal offsets relative to the unbroken general relativity benchmark are bounded within $\Delta R_{1.4}\in[-0.09,-0.01]\,\mathrm{km}$ and $\Delta\Lambda_{1.4}\approx -20.7$; after calibrating the solar-system asymptotic gravitational constant $G_\infty=G/(1+\xi)$ and subtracting the ground-state homologous scaling, the net observable offsets contributed purely by spatially inhomogeneous scalar polarization reduce to $|\delta R_{1.4}^{\mathrm{pol}}|<0.01\,\mathrm{km}$ and $|\delta\Lambda_{1.4}^{\mathrm{pol}}|\approx 0.12\text{--}0.58$, well below the resolution limits of current and third-generation (3G) multimessenger detectors. This study numerically establishes a quantitative upper bound on macroscopic deviations for such static non-zero-vacuum barrier models, confirming that tachyon-free massive scalar gravitational degrees of freedom naturally decouple in the strong-field core without artificial parameter fine-tuning and remain theoretically viable within modern multimessenger observational bounds.