Universal relations for quasinormal modes of neutron stars in $R^2$ gravity

Abstract: We construct quasinormal modes for neutron stars in $R^2$ gravity in the Einstein frame, considering scalar masses in the sub-neV range. In particular, we investigate the fundamental quadrupole fluid f-modes and the dipole fluid F-modes. Employing six equations of state covering matter content with nucleons, hyperons, and quarks, we then propose universal relations for the quadrupole f-modes and dipole F-modes. The dipole F-modes are ultra-long lived and, for the lower scalar masses, their frequencies are inversely proportional to the corresponding Compton wavelength.