Scalar models for the generalized Chaplygin gas and the structure formation constraints

TL;DR

This paper examines scalar field models for the generalized Chaplygin gas, analyzing their viability for unifying dark matter and dark energy, and explores constraints from structure formation and modifications inspired by Rastall's gravity.

Contribution

It introduces scalar field formulations of the generalized Chaplygin gas, addressing perturbative issues and proposing non-canonical models inspired by Rastall's theory to improve unification prospects.

Findings

Perturbative analysis restricts alpha to positive values.

Self-interacting scalar fields can avoid DBI limitations.

Non-canonical scalar fields align better with structure formation constraints.

Abstract

The generalized Chaplygin gas model represents an attempt to unify dark matter and dark energy. It is characterized by a fluid with an equation of state $p = - A/\rho^\alpha$. It can be obtained from a generalization of the DBI action for a scalar, tachyonic field. At background level, this model gives very good results, but it suffers from many drawbacks at perturbative level. We show that, while for background analysis it is possible to consider any value for $\alpha$, the perturbative analysis must be restricted to positive values of $\alpha$. This restriction can be circumvented if the origin of the generalized Chaplygin gas is traced back to a self-interacting scalar field, instead of the DBI action. But, in doing so, the predictions coming from formation of large scale structures reduce the generalized Chaplygin gas model to a kind of quintessence model, and the unification scenario is lost, if the scalar field is the canonical one. However, if the unification condition is imposed from the beginning as a prior, the model may remain competitive. More interesting results, concerning the unification program, are obtained if a non-canonical self-interacting scalar field, inspired by Rastall's theory of gravity, is imposed. In this case, an agreement with the background tests is possible.