Neutron star solutions in perturbative quadratic gravity

We study the structure of neutron stars in R+βR ^μνR _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) ^1/2 ∼ 10 ⁶ cm is of the order of the the typical radius of neutron stars, the probe used in this test. This implies that the true value of β is most likely much smaller than 10 ¹¹ cm ².