  The production of quantum field excitations or particles in cosmological
spacetimes is a hallmark prediction of curved quantum field theory. The
generation of cosmological perturbations from quantum fluctuations in the early
universe constitutes an important application. The problem can be
quantum-simulated in terms of structure formation in an interacting
Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length.
Here, we explore a mapping between cosmological particle production in general
(D+1)-dimensional spacetimes and scattering problems described by the
non-relativistic stationary Schr\"odinger equation in one dimension. Through
this mapping, intuitive explanations for emergent spatial structures in both
the BEC and the cosmological system can be obtained for a large class of
analogue cosmological scenarios, ranging from power-law expansions to periodic
modulations. The investigated cosmologies and their scattering analogues are
tuned to be implemented in a (2+1)-dimensional quantum field simulator.
