Due to their high degree of controllability and precise measurement capabilities, ultracold ensembles of neutral atoms are a leading platform for performing quantum simulations. In this thesis, I will describe the design and construction of an analog quantum simulator based on $^{23}$Na Bose-Einstein Condensates (BEC). Our system can produce and trap BECs in arbitrary-shaped quasi two-dimensional optical dipole traps, which can be dynamically altered during an experimental sequence. Such controlled variation of the BEC's spatial mode enables exploration of open questions in superfluidity, atomtronics, and analogue cosmology. I will describe the implementation of our system to study the inflationary dynamics of the early universe and report our recent results on the simulation of cosmological Hubble friction. We expand and contract a toroidally shaped BEC and analyze the time evolution of its collective phonon modes. These excitations are analogous to fluctuating scalar fields in an expanding universe. The changing metric of the expanding or contracting background BEC results in dilation of the phonon field through a term dependent on the expansion speed, similar to Hubble friction in inflationary models of the universe. We conclusively demonstrate the analogy by experimentally measuring Hubble attenuation and amplification. Our measured strength of Hubble friction disagrees with recent theoretical work [J. M. Gomez Llorente and J. Plata, {\it Phys. Rev. A} {\bf 100} 043613 (2019) and S. Eckel and T. Jacobson, {\it SciPost Phys.} {\bf 10} 64 (2021)], suggesting inadequacies in the current model.