I-Love-Q in Einstein-aether Theory

Einstein-aether theory is a modified theory of gravity which breaks gravitational Lorentz invariance by introducing a vector field called the aether. This vector field is unit, timelike and gives a preferred time direction at each point in space. Einstein-aether theory has four free parameters which characterize deviations from General Relativity 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 elusively unconstrained. The goal of this project is to see if it is feasible to use neutron star observations 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. To understand if the theory can be constrained through such relations, we derive the I-Love-Q quantities in Einstein-aether theory and see if any of them depend on cω.