Eur. Phys. J. Plus (2018) 133: 21
https://doi.org/10.1140/epjp/i2018-11861-y

Regular Article

Initial singularity and pure geometric field theories

¹ Astronomy Department, Faculty of Science, Cairo University, Giza, Egypt
² Mathematics Department, Faculty of Girls, Ain Shams University, Cairo, Egypt
³ Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

^* e-mail: wanas@scu.eg

Received: 16 December 2017
Accepted: 6 January 2018
Published online: 23 January 2018

Abstract

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.