The Hidden Flat Like Universe: Starobinsky-like inflation induced by f(T) gravity

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 the value of the spatial curvature $k$, identifies a special class of $f(T)$ gravity theories. Remarkably, the 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 (EoS) evolves similarly in all models $k=0,\pm 1$. We study the case when the torsion tensor is made 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) $n_s$ the theory can predict double tensor-to-scalar ratios $r$ of $E$-mode and $B$-mode polarizations.

LaTeX2e, 14 pages, 10 figures. Title modified, Major revision, References updated. To be appeared in EPJC

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• Phase Portraits of general f(T) Cosmology
• Exact Teleparallel Gravity of Binary Black Holes
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• Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology
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• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
• On the Expanding Phase of a Singular Bounce and Intermediate Inflation: The Modified Gravity Description