Quantum potential in bouncing dust collapse with a negative cosmological constant

Abstract

In the functional Schrodinger formalism, we obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer, by mapping the resulting variable mass Schrodinger equation to that of the quantum isotonic oscillator. Using this wave function, we perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. We construct a bouncing geometry via a disformal transformation, incorporating quantum effects. We derive the external solution that matches with this smoothly, and is also quantum corrected. Due to a pressure term originating from the quantum potential, an initially collapsing solution with a negative cosmological constant bounces back after reaching a minimum radius, and thereby avoids the classical singularity predicted by general relativity.