Further stable neutron star models from f(R) gravity
  Neutron star models in perturbative $f(R)$ gravity are considered with
realistic equations of state. In particular, we consider the FPS, SLy and other
equations of state and a case of piecewise equation of state for stars with
quark cores. The mass-radius relations for $f(R)=R+R(e^{-R/R_{0}}-1)$ model and
for $R^2$ models with logarithmic and cubic corrections are obtained. In the
case of $R^2$ gravity with cubic corrections, we obtain that at high central
densities ($\rho>10\rho_{ns}$, where $\rho_{ns}=2.7\times 10^{14}$ g/cm$^{3}$
is the nuclear saturation density), stable star configurations exist. The
minimal radius of such stars is close to $9$ km with maximal mass $\sim 1.9
M_{\odot}$ (SLy equation). A similar situation takes place for AP4 and BSK20
EoS. Such an effect can give rise to more compact stars than in General
Relativity. If observationally identified, such objects could constitute a
formidable signature for modified gravity at astrophysical level. Another
interesting result can be achieved in modified gravity with only a cubic
correction. For some EoS, the upper limit of neutron star mass increases and
therefore these EoS can describe realistic star configurations (although, in
General Relativity, these EoS are excluded by observational constraints).
