  Due to our ignorance of the equation of state (EOS) beyond nuclear density,
there is still no unique theoretical model for neutron stars (NSs). It is
therefore surprising that universal EOS-independent relations connecting
different physical quantities of neutron stars can exist. Lau et al. [ApJ, 714,
1234 (2010)] found that the frequency of the $f$-mode oscillation, the mass,
and the moment of inertia are connected by universal relations. More recently,
Yagi and Yunes [Science, 341, 365 (2013)] discovered the I-Love-Q universal
relations among the mass, the moment of inertia, the Love number, and the
quadrupole moment. In this paper, we study these universal relations in the
Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general
relativity (GR) significantly only at high densities due to the nonlinear
coupling between matter and gravity. It thus provides us an ideal case to test
how robust the universal relations of NSs are with respect to the change of the
gravity theory. Thanks to the apparent EOS formulation of EiBI gravity
developed recently by Delsate and Steinhoff [Phys. Rev. Lett., 109, 021101
(2012)], we are able to study the universal relations in EiBI gravity using the
same techniques as those in GR. We find that the universal relations in EiBI
gravity are essentially the same as those in GR. Our work shows that, within
the currently viable coupling constant, there exists at least one modified
gravity theory that is indistinguishable from GR in view of the unexpected
universal relations.
