  This study focuses on the static neutron star perspective for two types of
cosmological inflationary attractor theories, namely the induced inflationary
attractors and the quadratic inflationary attractors. The two cosmological
models can be discriminated cosmologically, since one of the two does not
provide a viable inflationary phenomenology, thus in this paper we investigate
the predictions of these theories for static neutron stars, mainly focusing on
the mass and radii of neutron stars. We aim to demonstrate that although the
models have different inflationary phenomenology, the neutron star
phenomenology predictions of the two models are quite similar. We solve
numerically the Tolman-Oppenheimer-Volkoff equations in the Einstein frame
using a powerful double shooting numerical technique, and after deriving the
mass-radius graphs for three types of polytropic equations of state, we derive
the Jordan frame mass and radii. With regard the equations of state we use
polytropic equation of state with the small density part being either the WFF1,
the APR or the intermediate stiffness equation of state SLy. The results of our
models will be confronted with quite stringent recently developed constraints
on the radius of neutron stars with specific mass. As we show, the only
equation of state which provides results compatible with the constraints is the
SLy, for both the quadratic and induced inflation attractors. Thus nowadays,
scalar-tensor descriptions of neutron stars are quite scrutinized due to the
growing number of constraining observations, which eventually may also
constrain theories of inflation.
