Analog models provide another point of view to approach problems. They play a very important role in physics and mathematics, since they allow us to study and observe phenomena that are not directly accessible. In this talk, we will address the problem of cosmological particle production in curved and expanding universes, specifically, in expanding Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies, using such analogies. It is common, although not strictly necessary, to use condensed matter systems to obtain information on these phenomena, since they can be realized experimentally and are well-controlled systems. In this case, we choose Bose-Einstein condensates (BECs) to mimic their dynamical aspects. In particular, we study low-momentum excitations of BECs (phonons), which have a linear dispersion relation as massless relativistic particles. Their dynamics is described by an acoustic metric and we investigate the mapping between this metric and that of a spatially curved FLRW universe. In essence, we show that cosmological particle production and many other quantum phenomena can be studied by simulating them in a condensate and can be confirmed experimentally.