Abstract. We study the structure of neutron stars in R + βR µν R µν gravity model with perturbative method. We obtain mass-radius relations for six representative equations of state (EoSs). We find that, for |β| ∼ 10 11 cm 2 , the results differ substantially from the results of general relativity. Some of the soft EoSs that are excluded within the framework of general relativity can be reconciled for certain values of β of this order with the 2 solar mass neutron star recently observed. For values of β greater than a few 10 11 cm 2 we find a new solution branch allowing highly massive neutron stars. By referring some recent observational constraints on the mass-radius relation we try to constrain the value of β for each EoS. The associated length scale √ β ∼ 10 6 cm is of the order of the the typical radius of neutron stars implying that this is the smallest value we could find by using neutron stars as a probe. We thus conclude that the true value of β is most likely much smaller than 10 11 cm 2 .

We investigate the effect of a strong magnetic field on the structure of neutron stars in a model with perturbative f (R) gravity. The effect of an interior strong magnetic field of about 10 17∼18 G on the equation of state is derived in the context of a quantum hadrodynamics (QHD) model. We solve the modified spherically symmetric hydrostatic equilibrium equations derived for a gravity model with f (R) = R + αR 2 .Effects of both the finite magnetic field and the modified gravity are detailed for various values of the magnetic field and the perturbation parameter α along with a discussion of their physical implications. We show that there exists a parameter space of the modified gravity and the magnetic field strength, in which even a soft equation of state can accommodate a large (> 2 M ⊙ ) maximum neutron star mass through the modified mass-radius relation.

Abstract.We addressed possible ambiguities on the properties of neutron stars (NSs) estimated in theoretical sides. First, roles of hyperons inside the NS are discussed through various relativistic mean field (RMF) theories. In particular, the extension of SU(6) spin-flavor symmetry to SU(3) flavor symmetry is shown to give rise to the increase of hyperon threshold density, similarly to the Fock term effects in RMF theories. As a result, about 2.0 solar mass is obtained with the hyperons. Second, the effect by the modified f(R) gravity, which leaves a room for the dark energy in the Einstein equation to be taken into account, is discussed for the NS in a strong magnetic field (MF). Our results show that the modified gravity with the Kaluza-Klein electro-magnetism theory expanded in terms of a length scale parameter may reasonably describe the NS in strong MF, so called magnetar. Even the super-soft equation of state is shown to be revived by the modified f(R) gravity.