  We study the structure of neutron stars in f(R) gravity theories with
perturbative constraints. We derive the modified Tolman-Oppenheimer-Volkov
equations and solve them for a polytropic equation of state. We investigate the
resulting modifications to the masses and radii of neutron stars and show that
observations of surface phenomena alone cannot break the degeneracy between
altering the theory of gravity versus choosing a different equation of state of
neutron-star matter. On the other hand, observations of neutron-star cooling,
which depends on the density of matter at the stellar interior, can place
significant constraints on the parameters of the theory.
