  We perform an analysis of the supercooled state in an analogue of an early
universe phase transition based on a one dimensional, two-component Bose gas
with time-dependent interactions. We demonstrate that the system behaves in the
same way as a thermal, relativistic Bose gas undergoing a first order phase
transition. We propose a way to prepare the state of the system in the
metastable phase as an analogue to supercooling in the early universe. While we
show that parametric resonances in the system can be suppressed by thermal
damping, we find that the theoretically estimated thermal damping in our model
is too weak to suppress the resonances for realistic experimental parameters.
However, we propose that experiments to investigate the effective damping rate
in experiments would be worthwhile.
