A model for an expanding noncommutative acoustic fluid analogous to a Friedmann-Robertson-Walker geometry is derived. For this purpose, a noncommutative Abelian Higgs model is considered in a ($3+1$)-dimensional spacetime. In this scenario, we analyze the motion of test particles in this fluid. The study considers a scalar test particle coupled to a quantized fluctuating massless scalar field. For all cases studied, we find corrections due to the noncommutativity in the mean squared velocity of the particles. The nonzero velocity dispersion for particles that are free to move on geodesics disagrees with the null result found previously in the literature for expanding commutative fluid.

中文翻译：

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膨胀的非对易流体中的随机运动

导出了类似于 Friedmann-Robertson-Walker 几何的膨胀非对易声学流体模型。为此，在 ($3+1$)维时空。在这种情况下，我们分析测试粒子在该流体中的运动。该研究考虑了与量化波动的无质量标量场耦合的标量测试粒子。对于所有研究的案例，我们发现由于粒子均方速度的非对易性而进行了修正。可在测地线上自由移动的粒子的非零速度色散与之前在文献中发现的用于扩展交换流体的零结果不一致。