  $f(R)$ 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 non-perturbative and self-consistent. The neutron star
properties, such as mass, radius and moment of inertia, are studied in detail
and 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 previous studies of rapidly rotating
neutron stars in other alternative theories of gravity, such as the
scalar-tensor theories, and it can potentially lead to strong astrophysical
manifestations.
