Phonon dynamics in spherically-curved analog-gravity Bose–Einstein condensates

We study the low energy phonon dynamics of a Bose–Einstein condensate (BEC) with a density profile that is equivalent, via a coordinate transformation, to phonons traveling in a “spherical” curved spacetime that realizes the Friedman–Lemaître–Robertson–Walker (FLRW) metric. The metric of this BEC is characterized by its curvature κ κ and a time-dependent scale factor a ( t ), with an increase in the latter corresponding to an expansion of the analog FLRW universe. We study the propagation of classical phonons in such BECs, finding that a sudden change in the scale factor induces ripples in the wave motion. In addition, we study quantum phonon creation (or vacuum amplification) due to the scale-factor modification and quantify their entanglement.