$f(R)$ theories of gravity are one of the most popular alternative explanations for dark energy, and therefore studying the possible astrophysical implications of these theories is an important task. In the present paper we make a substantial advance in this direction by considering rapidly rotating neutron stars in $R^2$ gravity. The results are obtained numerically, and the method we use is nonperturbative and self-consistent. The neutron star properties, such as mass, radius, and moment of inertia, are studied in detail. The results show that rotation magnifies the deviations from general relativity, and the maximum mass and moment of inertia can reach very high values. This observation is similar to the previous studies of rapidly rotating neutron stars in other alternative theories of gravity, such as scalar-tensor theories, and it can potentially lead to strong astrophysical manifestations.

• Received 27 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.084018