The neutron star solutions have been gathering attention. Their high compactness enables us to observationally access the information about extreme regimes of hadron physics. On the other hand, their strong gravity features bring up another possibility, gravity beyond general relativity (GR). Although GR has been a great success until now, the present scenario for our universe still has several problems, such as dark sectors and the quantum description of gravity. To tackle these problems, the modified gravity theories have been discussed for decades. Their modifications are expected to become noticeable in strong gravity regimes like compact stars.

In this talk, I will discuss the configuration of the compact star solution under the F(R) gravity, one of the most popular and simplest modifications of GR. The background hydrostatic solutions are calculated with some F(R) models, which show non-trivial influences from the additional scalar DOF in this theory. Furthermore, I will discuss how to utilize observables to determine gravity theories and the unknown equation of state simultaneously.