I-Love-Q in Einstein-aether theory

Although local Lorentz invariance 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. A way to investigate and test Lorentz symmetry violation is to study it within modifications to GR. One such modified theory is Einstein-aether theory, which breaks Lorentz symmetry by introducing a dynamical vector field called the aether. The aether is timelike and points out a preferred time direction at each point in space. Einstein-aether theory has four coupling constants that characterize deviations from GR and which must be determined, or constrained, by experimental observations. Although three of the four parameters have been constrained by various empirical observations and stability requirements, one, called cω, remains unconstrained. The goal of this work is to see if it is feasible to use neutron star observables to constrain cω. Specifically, we aim to see if a constraint can be derived from the I-Love-Q universal relations, which are relations between the neutron star moment of inertia (I), tidal Love number (Love), and quadrupole moment (Q). These relations are useful for utilizing neutron star observables because they are insensitive to uncertainties in the neutron star equation-of-state. We find that the I-Love-Q relations in Einstein-aether theory are insensitive to cω and that they are close to the relations in GR. These results indicate that to constrain the theory with neutron stars, it is necessary to investigate other relations and observables, such as stellar oscillation frequencies.