Stiff Fluid in Accelerated Universes with Torsion

Almaz Galiakhmetov

doi:10.1155/2013/306417

Abstract

The flat Friedmann universes filled by stiff fluid and a nonminimally coupled material scalar field with polynomial potentials of the fourth degree are considered in the framework of the Einstein-Cartan theory. Exact general solution is obtained for arbitrary positive values of the coupling constant . A comparative analysis of the cosmological models with and without stiff fluid is carried out. Some effects of stiff fluid are elucidated. It is shown that singular models with a de Sitter asymptotic and with the power-law asymptotic at late times are possible. It is found that is a specific value of the coupling constant. It is demonstrated that the bouncing models without the particle horizon and with an accelerated expansion by a de Sitter law of an evolution at late times are admissible.

Highlights

Recent cosmic observations [1,2,3,4,5,6] favor an isotropic spatially flat Universe, which is at present expanding with acceleration
In the framework of the Einstein-Cartan theory (ECT) with a nonminimally coupled material scalar field that has polynomial potentials of the fourth degree, we here study isotropic spatially flat cosmologies in which stiff fluid is taken into account
In order to elucidate the role of the stiff fluid in the Einstein-Cartan cosmology, we should carry out a comparative analysis of the corresponding cosmological models obtained in this paper and those in [12] for “Scalar-torsion field” and in [13] for “Scalar-torsion field” + “V(Φ).”

Summary

Introduction

Recent cosmic observations [1,2,3,4,5,6] favor an isotropic spatially flat Universe, which is at present expanding with acceleration. In the framework of the ECT with a nonminimally coupled material scalar field that has polynomial potentials of the fourth degree, we here study isotropic spatially flat cosmologies in which stiff fluid is taken into account. The motivation to investigate a nonminimally coupled scalar field is based on the results obtained within the framework of the torsionless theories of gravity in connection with the inflationary cosmology (see, e.g., [50,51,52,53,54]) and DE model building [55,56,57]. The exact general solutions for spatially flat FRW cosmologies with a nonminimally coupled scalar field that has polynomial potentials of the fourth degree V(Φ) have been obtained in [13].

Field Equations

Exact Solution

Conclusion