  The Higgs scalar which is the only experimentally verified fundamental
cosmological scalar, is also known to produce a viable inflationary
phenomenology. In this work we investigate the effects of the Higgs model on
static neutron stars. Particularly we derive the Einstein frame
Tolman-Oppenheimer-Volkoff equations, and by numerically integrating them for
both the interior and the exterior of the neutron star, using a double shooting
python 3 based numerical code, we extract the masses and radii of the neutron
stars, along with the several other related physical quantities of interest.
With regard to the equation of state for the neutron star, we use a piecewise
polytropic equation of state with the central part being SLy, APR or the WFF1
equations of state. The resulting $M-R$ graphs are compatible with the
observational bounds imposed by the GW170817 event which require the radius of
a static $M\sim 1.6 M_{\odot}$ neutron star to be larger than
$R=10.68^{+15}_{-0.04}$km and the radius of a static neutron star corresponding
to the maximum mass of the star to be larger than $R=9.6^{+0.14}_{-0.03}$km.
Moreover, the WFF1 EoS, which was excluded for static neutron stars in the
context of general relativity, for the Higgs neutron star model provides
realistic results compatible with the GW170817 event.
