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We analytically study the expansion of a Bose-Einstein condensate in aring-shaped trap with an increasing central radius. The evolution of the groundstate is described using a scaling transform. Additionally, the dynamics ofexcited azimuthal modes over the varying ground state is analyzed through ageneralization of the Bogoliubov-de Gennes approach. Our results explain someof the features observed in recent experiments focused on testing theapplicability of the system as a parallel of cosmological inflationary models.The radial dynamics, which corresponds to the inflaton field of thecosmological counterpart, is analytically characterized: The expansion is foundto induce the oscillatory displacement of the condensate as well as the coupledvariation of the radial and vertical widths. Our findings account also for theobserved redshift and emergence of the Hubble friction in the evolution ofinitially-prepared azimuthal modes. Our description, which traces the role ofthe different components of the setup in the expansion, enhances thecontrollability, and, therefore, the potential of the system as a ground foremulating the inflationary dynamics of cosmological models.

Expanding ring-shaped Bose-Einstein condensates as analogs of cosmological models: Analytical characterization of the inflationary dynamics