The Chaplygin gas as a model for modified teleparallel gravity?

TL;DR

This paper investigates whether the Chaplygin gas model can be represented within $f(T)$ teleparallel gravity, reconstructing corresponding Lagrangians and analyzing the evolution of the torsion fluid's equation of state.

Contribution

It demonstrates how to reconstruct $f(T)$ Lagrangians from Chaplygin gas models and explores their cosmological implications as dark matter and dark energy.

Findings

Reconstructed $f(T)$ Lagrangians depend on matter and torsion.

Chaplygin gas solutions mimic dark matter and dark energy behaviors.

The method can address challenges in Chaplygin gas cosmology.

Abstract

This paper explores the possibility of treating the exotic Chaplygin-gas (CG) fluid model as some manifestation of an $f(T)$ gravitation. To this end, we use the different cosmological CG equations of state, compare them with the equation of state for the modified teleparallel gravity and reconstruct the corresponding Lagrangian densities. We then explicitly derive the equation of state parameter of the torsion fluid $w_T$ and study its evolution for vacuum-torsion, radiation-torsion, dust-torsion, stiff fluid torsion, and radiation-dust-torsion multi-fluid systems. The obtained Lagrangians have, in general, matter dependence due to the matter-torsion coupling appearing in the energy density and pressure terms of the modified teleparallel gravity theory. For the simplest CG models, however, it is possible to reconstruct $f(T)$ Lagrangians that depend explicitly on the torsion scalar $T$ only. The preliminary results show that, in addition to providing Chaplygin-gas-like solutions to the modified teleparallel gravitation, which naturally behave like dark matter and dark energy at early and late times respectively, the technique can be used to overcome some of the challenges attributed to the CG cosmological alternative.