JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS, no.7, 2011 (Journal Indexed in SCI)
We study the structure of neutron stars in perturbative (R) gravity models with realistic equations of state. We obtain mass-radius relations in a gravity model of the form f(R) = R + alpha R-2. We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state (EoS'), are induced for |alpha| similar to 10(9) cm(2). Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of alpha within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of alpha greater than a few 10(9) cm(2). We find constraints on alpha for a variety of EoS' using the recent observational constraints on the mass-radius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale root alpha similar to 10(5) cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that, real deviations from general relativity can be even smaller.