  We consider two weakly interacting quasi-1D condensates of cold bosonic
atoms. It turns out that a time-dependent variation of the tunnel-coupling
between those condensates is equivalent with the spatial expansion of a
one-dimensional toy-Universe with regard to the dynamics of the relative phase
field. The dynamics of this field is governed by the quantum sine-Gordon
equation. Thus, this analogy could be used to 'quantum simulate' the dynamics
of a scalar, interacting quantum field on an expanding background. We discuss,
how to observe the freezing out of quantum fluctuations during an accelerating
expansion in a possible experiment. We also discuss an experimental protocol to
study the formation of sine-Gordon breathers in the relative phase field out of
quantum fluctuations.
