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 possibly 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.
Highlights
In the general relativity (GR) approach, T is assumed to vanish and in teleparallel gravity (TG) theory, R is assumed to vanish [7]
The layout of the manuscript is as follows: we review the cosmology of f (T ) gravity together with the simplest CG cosmological models and relate the two through some sort of a master equation, which we solve in Sect. (2.1) for different cases
We present the reconstructed different Lagrangian density of f (T ) gravity models from Eq (222) for original CG (OCG) and Generalized CG (GCG) models as we did in the previous sections
Summary
In the general relativity (GR) approach, T is assumed to vanish and in TG theory, R is assumed to vanish [7]. Generalizations to the TG theory have been introduced in the form of f (T ) gravity, where the action is a generic function of T , rather than T itself. Together with a Friedman–Lemaître–Robertson– Walker (FLRW) background in the GR framework, this model can explain the cosmic expansion history for a Universe filled with an exotic background fluid [23,24,25,26,27,28,29], but has recently been studied in the context of modified gravity theories as well [27,28,30]. After obtaining the reconstructed f (T ) gravity models, we study the expansion dynamics of the Universe by calculating the energy density, pressure and equation of state parameter for the torsion fluid in the non-interacting fluid systems such as vacuum-torsion, radiation-torsion, dust-torsion and radiation-dust-torsion systems for the three variants of the CG model. We devote Sect. (4) for discussions of our results and the conclusions
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