Broken Lorentz symmetry

As particle physicists, we are familiar with gauge theory, which is based on exact symmetries usually described by compact groups. As cosmologists, however, we also need to deal with spacetime symmetries, which are typically non-compact. Lorentz symmetry, SO(1,3), is one such example. It contains six generators: three corresponding to spatial rotation symmetry and three corresponding to Lorentz boost symmetry. The spontaneous symmetry breaking pattern of Lorentz symmetry, together with some internal symmetry, can naturally lead to effective field theories of superfluids, solids, and fluids [1].

Among them, the simplest way to break the boost symmetry leads to the framid theory, also referred to as Einstein-aether theory. In these theories, a vector with fixed norm to avoid tachyonic instability acquires a vacuum expectation value that spontaneously breaks Lorentz boost symmetry. In flat space, the energy-momentum tensor of the aether background vanishes, but modifications to gravitational waves still appear. In an expanding universe, the aether field effectively “slows down” the expansion by rescaling Newton’s constant. In other words, the broken Lorentz boost symmetry provides a dynamical preferred inertial frame in which we observe the rest of the universe. Since it is purely in the gravity sector, this broken symmetry has not yet been verified or falsified.

We recently found a new coupling between the framid and a scalar field that exhibits fractonic symmetry, which may serve as a dark matter candidate. Further test is under investigation.