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Neutron star models in perturbative $f(R)$ gravity are considered withrealistic equations of state. In particular, we consider the FPS, SLy and otherequations of state and a case of piecewise equation of state for stars withquark cores. The mass-radius relations for $f(R)=R+R(e^{-R/R_{0}}-1)$ model andfor $R^2$ models with logarithmic and cubic corrections are obtained. In thecase of $R^2$ gravity with cubic corrections, we obtain that at high centraldensities ($\rho>10\rho_{ns}$, where $\rho_{ns}=2.7\times 10^{14}$ g/cm$^{3}$is the nuclear saturation density), stable star configurations exist. Theminimal radius of such stars is close to $9$ km with maximal mass $\sim 1.9M_{\odot}$ (SLy equation). A similar situation takes place for AP4 and BSK20EoS. Such an effect can give rise to more compact stars than in GeneralRelativity. If observationally identified, such objects could constitute aformidable signature for modified gravity at astrophysical level. Anotherinteresting result can be achieved in modified gravity with only a cubiccorrection. For some EoS, the upper limit of neutron star mass increases andtherefore these EoS can describe realistic star configurations (although, inGeneral Relativity, these EoS are excluded by observational constraints).

Further stable neutron star models from f(R) gravity