FRW Quantum Cosmology with a Generalized Chaplygin Gas

TL;DR

This paper explores quantum cosmological models with a generalized Chaplygin gas, analyzing wave functions and transition amplitudes to understand the universe's transition to accelerated expansion, and linking parameters to brane-world scenarios.

Contribution

It introduces a quantum framework for FRW cosmology with a generalized Chaplygin gas, identifying conditions for transitions and relating parameters to brane-world models.

Findings

Identified minisuperspace with two Lorentzian sectors separated by a classically forbidden region.

Computed Hartle-Hawking and Vilenkin wave functions for the model.

Linked Chaplygin gas parameters and brane tension to integer-related expressions.

Abstract

Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the accelerated period involves a quantum mechanical process. Three physically admissible cases are possible. In particular, we identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle-Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, it is found that for specific initial conditions, the parameters characterizing the generalized Chaplygin gas become related through an expression involving an integer $n$. We also introduce a phenomenological association between some brane-world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. The aim is to promote a discussion and subsequent research on the quantum creation of brane cosmologies from such a perspective. Results suggest that the brane tension would become related with generalized Chaplygin gas parameters through another expression involving an integer.