  Phonons in expanding Bose-Einstein condensates with wavelengths much larger
than the healing length behave in the same way as quantum fields within a
universe undergoing an accelerated expansion. This analogy facilitates the
application of many tools and concepts known from general relativity (such as
horizons) and the prediction of the corresponding effects such as the freezing
of modes after horizon crossing and the associated amplification of quantum
fluctuations. Basically the same amplification mechanism is (according to our
standard model of cosmology) supposed to be responsible for the generation of
the initial inhomogeneities -- and hence the seeds for the formation of
structures such as our galaxy -- during cosmic inflation (i.e., a very early
epoch in the evolution of our universe). After a general discussion of the
analogy (\emph{analogue cosmology}), we calculate the frozen and amplified
density-density fluctuations for quasi-two dimensional (Q2D) and three
dimensional (3D) condensates which undergo a free expansion after switching off
the (longitudinal) trap. PACS: 03.75.Kk, 04.62.+v.
