Hamilton-Jacobi formalism for Generalized Chaplygin Gas models

TL;DR

This paper applies the Hamilton-Jacobi formalism to Generalized Chaplygin Gas models with a scalar field, revealing their ability to mimic dark energy and matter behaviors, and exploring the effects of non-standard kinetic terms and scalar potentials.

Contribution

It introduces a Hamilton-Jacobi approach to GCG models with a scalar field, including a scalar potential, and analyzes their cosmological behavior and ability to replicate DM.

Findings

Asymptotic de Sitter-like solutions can occur with negative potentials.

The model can mimic DM at the background level.

Non-standard kinetic terms influence the cosmological dynamics.

Abstract

In this work we discuss the application of the Hamilton-Jacobi formalism on the scalar field implementation of Generalized Chaplygin Gas models. This corresponds to a Generalised Born-Infeld action for the scalar field, which in an initial fast-rolling phase mimics a matter-like behavior and in the final slow-rolling phase mimics a cosmological constant. In order to enrich the phenomenology of the model, we add an extra functional freedom, specified through a scalar potential for the field. Interestingly, we find that, due to the lifting induced by the non-standard kinetic term, an asymptotic de Sitter-like configuration can be obtained even for negative potentials. We show that at the background level, this model can easily mimic the {\Lambda}CDM model both with and without independent baryonic and radiation components.