A realistic model of a neutron star in minimal dilatonic gravity

We present a derivation of the basic equations and boundary conditions for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) which offers an alternative and simultaneous description of the effects of dark matter (DM) and dark energy (DE) using one dilaton field $\Phi$. The numerical results for a realistic equation of state (EOS) MPA1 of neutron matter are presented for the first time. The three very different scales, the Compton length of the scalar field $\lambda_\Phi$, the star's radius $r^*$, and the finite radius of the MDG Universe $r_{U}$ are a source of numerical difficulties. Owing to the introduction of a new dark scalar field $\varphi=\ln(1+\ln\Phi)$, we have been able to study numerically an unprecedentedly large interval of $\lambda_\Phi$ and have discovered the existence of $\lambda_\Phi^{crit}\approx 2.1$\ km for a neutron star with MPA1 EOS. This is related to the bifurcation of the physical domain in the phase space of the system. Some novel physical consequences are discussed.