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Phonons in expanding Bose-Einstein condensates with wavelengths much largerthan the healing length behave in the same way as quantum fields within auniverse undergoing an accelerated expansion. This analogy facilitates theapplication of many tools and concepts known from general relativity (such ashorizons) and the prediction of the corresponding effects such as the freezingof modes after horizon crossing and the associated amplification of quantumfluctuations. Basically the same amplification mechanism is (according to ourstandard model of cosmology) supposed to be responsible for the generation ofthe initial inhomogeneities -- and hence the seeds for the formation ofstructures such as our galaxy -- during cosmic inflation (i.e., a very earlyepoch in the evolution of our universe). After a general discussion of theanalogy (\emph{analogue cosmology}), we calculate the frozen and amplifieddensity-density fluctuations for quasi-two dimensional (Q2D) and threedimensional (3D) condensates which undergo a free expansion after switching offthe (longitudinal) trap. PACS: 03.75.Kk, 04.62.+v.Comment: 17 page

Aspects of cosmic inflation in expanding Bose–Einstein condensates