This paper addresses the process of Jeans gravitational instability in the framework of Eddington-inspired Born-Infeld (EiBI) theory, by accounting for quantum effects. In the Newtonian limit, the model reduces to a generalized Schrdinger-Poisson model, which is treated in two different ways: from a quantum hydrodynamic approach and from a quantum kinetic approach, based on the Wigner (quasi-)distribution. We show that, depending on the sign of κ, EiBI gravity leads to more or less stable structures: For , EiBI gravity produces a pressure-like term that acts, together with quantum pressure, against gravity, leading to more stable structures, while for the effect goes in the opposite direction. Our approach reproduces correctly the classical hydrodynamic and kinetic results in the proper limits, which is made more transparent by introducing a nonlinear Schrdinger equation accounting for the degree of quantumness. Our results may open up a novel route for probing EiBI gravity in dense astrophysical media, where quantum effects are no longer negligible.

本文通过考虑量子效应，在受 Eddington 启发的 Born-Infeld (EiBI) 理论框架内解决 Jeans 引力不稳定性的过程。在牛顿极限下，该模型简化为广义 Schrdinger-Poisson 模型，以两种不同的方式对其进行处理：从量子流体动力学方法和从基于 Wigner（准）分布的量子动力学方法。我们表明，取决于符号κ，EiBI重力导致或多或少的稳定结构：对于，EiBI重力产生的压力般的术语，行为，与量子压在一起，对抗地心引力，导致更稳定的结构，而对于效果则相反。我们的方法在适当的限制中正确地再现了经典的流体动力学和动力学结果，通过引入考虑量子程度的非线性 Schrdinger 方程，这变得更加透明。我们的结果可能为在密集的天体物理介质中探测 EiBI 引力开辟了一条新途径，在这种介质中量子效应不再可以忽略不计。