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We study the structure of neutron stars in perturbative f(R) gravity modelswith realistic equations of state. We obtain mass-radius relations in a gravitymodel of the form f(R)=R+\alpha R^2. We find that deviations from the resultsof general relativity, comparable to the variations due to using differentequations of state (EoS'), are induced for |alpha| ~ 10^9 cm^2. Some of thesoft EoS' that are excluded within the framework of general relativity can bereconciled with the 2 solar mass neutron star recently observed for certainvalues of alpha within this range. For some of the EoS' we find that a newsolution branch, which allows highly massive neutron stars, exists for valuesof alpha greater than a few 10^9 cm^2. We find constraints on alpha for avariety of EoS' using the recent observational constraints on the mass-radiusrelation. These are all 5 orders of magnitude smaller than the recentconstraint obtained via Gravity Probe B for this gravity model. The associatedlength scale \sqrt{alpha} ~ 10^5 cm is only an order of magnitude smaller thanthe typical radius of a neutron star, the probe used in this test. This impliesthat real deviations from general relativity can be even smaller.

Constraints on Perturbative f(R) Gravity via Neutron Stars