Eur. Phys. J. C (2015) 75: 279
https://doi.org/10.1140/epjc/s10052-015-3501-y

Regular Article - Theoretical Physics

The hidden flat like universe

Starobinsky-like inflation induced by f (T) gravity

¹ Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, El Sherouk, 11837, Egypt
² Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt
³ Egyptian Relativity Group, Giza, Egypt

^* e-mail: nashed@bue.edu.eg

Received: 10 April 2015
Accepted: 2 June 2015
Published online: 24 June 2015

Abstract

We study a single-fluid component in a flat like universe (FLU) governed by f(T) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f(T) gravity theories. Remarkably, FLU f(T) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models . We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f(T) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations.