  Although Lorentz symmetry is a staple of General Relativity (GR), there are
several reasons to believe it may not hold in a more advanced theory of
gravity, such as quantum gravity. Einstein-aether theory is a modified theory
of gravity that breaks Lorentz symmetry by introducing a dynamical vector field
called the aether. The theory has four coupling constants that characterize
deviations from GR and that must be determined through observations. Although
three of the four parameters have been constrained by various empirical
observations and stability requirements, one, called $c_\omega$, remains
essentially unconstrained. The aim of this work is to see if a constraint on
$c_\omega$ can be derived from the I-Love-Q universal relations for neutron
stars, which connect the neutron star moment of inertia (I), the tidal Love
number (Love), and the quadrupole moment (Q) in a way that is insensitive to
uncertainties in the neutron star equation-of-state. To understand if the
theory can be constrained through such relations, we model slowly-rotating or
weakly tidally-deformed neutron stars in Einstein-aether theory, derive their
I-Love-Q relations, and study how they depend on $c_\omega$. We find that the
I-Love-Q relations in Einstein-aether theory are insensitive to $c_\omega$ and
that they are close to the relations in GR. This means that the I-Love-Q
relations in Einstein-aether theory remain universal but cannot be used to
constrain the theory. These results indicate that to constrain the theory with
neutron stars, it is necessary to investigate relations involving other
observables.
