Jeans instability in Eddington-inspired Born-Infeld (EiBI) gravity: a quantum approach

Abstract

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 Schrödinger-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 Schrödinger 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.