The gravitational aether theory is a modification of general relativity that decouples vacuum energy from gravity, and thus can potentially address the cosmological constant problem. The classical theory is distinguishable from general relativity only in the presence of relativistic pressure (or vorticity). Since the interior of neutron stars has high pressure and as their mass and radius can be measured observationally, they are the perfect laboratory for testing the validity of the aether theory. In this paper, we solve the equations of stellar structure for the gravitational aether theory and find the predicted mass-radius relation of non-rotating neutron stars using two different realistic proposals for the equation of state of nuclear matter. We find that the maximum neutron star mass predicted by the aether theory is 12% - 16% less than the maximum mass predicted by general relativity assuming these two equations of state. We also show that the effect of aether is similar to modifying the equation of state in general relativity. The effective pressure of the neutron star given by the aether theory at a fiducial density differs from the values given by the two nuclear equations of state to an extent that can be constrained using future gravitational wave observations of neutron stars in compact systems. This is a promising way to test the aether theory if further progress is made in constraining the equation of state of nuclear matter in densities above the nuclear saturation density.

8 pages, 6 figures