Cosmological perturbations and gravitational waves in the general Einstein-vector theory

Abstract

We investigate the stability and gravitational waves (GWs) in the four-dimensional general Einstein-vector theory on a cosmological background. To study the stability, we systematically perform a Hamiltonian analysis at the linear perturbation level. The stability conditions are easily satisfied for tensor perturbations, but they impose nontrivial constraints on the parameter space for vector and scalar perturbations. In particular, in the presence of a nonzero background vector field, the scalar sector fails to satisfy the stability conditions in the general parameter space. However, imposing the plane-wave condition relaxes these conditions, making them achievable. In the small-scale limit, we further investigate the GW properties of the general Einstein-vector theory within the stable parameter space, including the number of independent modes, their propagation speeds, and observational constraints from GW experiments. We find that there can be at most two tensor modes, two vector modes, and one scalar mode. Notably, without imposing the plane-wave ansatz, no scalar GWs exist within the stable parameter space. Furthermore, vector GWs are forbidden if tensor GWs propagate exactly at the speed of light.