Sigma-model aether

Theories of low-energy Lorentz violation by a fixed-norm “aether” vector field with two-derivative kinetic terms have a globally bounded Hamiltonian and are perturbatively stable only if the vector is timelike and the kinetic term in the action takes the form of a sigma model. Here we investigate the phenomenological properties of this theory. We first consider the propagation of modes in the presence of gravity and show that there is a unique choice of curvature coupling that leads to a theory without superluminal modes. Experimental constraints on this theory come from a number of sources, and we examine bounds in a two-dimensional parameter space. We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constant-density hypersurfaces in a Friedmann-Robertson-Walker cosmology. Finally, we examine cosmological evolution in the presence of an extra compact dimension of space, concluding that a vector can maintain a constant projection along the extra dimension in an expanding universe only when the expansion is exponential.

Figure 1

Aether rest-frame mode phase velocities squared, $v^2$, minus the speed of light in units of $8\pi G{m}^2$ as a function of $\alpha$. The solid (red) line corresponds to spin-0, the small dashed line (green) to spin-1, and the large dashed line (blue) to spin-2. Only for $\alpha =-1$ do none of the modes propagate faster than light ($v^2-1>0$).

Figure 2

Parameter space allowed (shaded region) by constraints from Čerenkov radiation and PPN. The strongest constraint in the $\alpha <-1$ region is from Eq. (17), and for most of the $\alpha >-1$ region the strongest constraint is from the second inequality in Eq. (18). The plot on the right is a blowup of the small range of $\alpha$ for which the first constraint in Eq. (18) is strongest—when $\alpha =-1$ to within a couple of parts in 100.