  In this project, we try to find the correlation between the non-local
pressure inside the massive neutron stars resisting the gravitational collapse
of the core and ECSK dark energy led by the effect of spin-torsion coupling
between quark fields and the space-time at very high densities much larger than
the nuclear density. The injection of dark energy into the core of massive
neutron stars (MANs) and extra resistant nature of this dark energy to the
collapse of MANs by the anti-gravity give the possibility of existence of
neutron stars in the unobserved mass range of $[2.16M_{\odot},5M_{\odot}]$.
Obtaining the ECSK TOV equation gives the local pressure of the ambient medium
of MANs. Moreover, the negative pressure from the ECSK dark energy is obtained
from the Lagrangian again, from which we are able to investigate the
hydro-static equilibrium of the core and ambient medium of the MANs. If the
equilibrium state is satisfied for the unobserved mass gap for the MANs in ECSK
theory framework this will imply our model predicts this vast mass range of
unobserved spectrum of the MANs in astrophysical studies.
