Bosons in fluctuating gauge fields: Bose metal and phase separation

We study a two-dimensional system of bosons interacting with a fluctuating U(1) gauge field with overdamped dynamics. We find two instabilities of the condensed phase at T=0: one to phase separation and another to a homogeneous non-superfluid (Bose metal). The presence of both instabilities in the model is dependent on the low-energy form of the gauge field propagator. We discuss the relevance of our findings to the U(1) gauge theory of the t--J model.