Recent theoretical studies of an expanding quark-gluon plasma, utilizing the Müller-Israel-Stewart formalism, have given rise to the concept of hydrodynamic attractors in relativistic viscous hydrodynamics. In parallel, the Son-Nicolis framework has elucidated the relation between fields and thermodynamical variables in an effective field theory. Expanding upon the incorporation of both approaches, we study the theory of an effective action for a complex scalar field, charged under a $U(1)$ global symmetry with a temperature-dependent symmetry-breaking potential, giving rise to a phase transition, in expanding background metrics. In particular, we examine the evolution of this superfluid within the contexts of Bjorken flow, Gubser flow, and the Friedmann-Lemaître-Robertson-Walker background, with special emphasis on the estimation of the hydrodynamic attractor timescale and the oscillatory behavior across these scenarios.
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