A Built-in Inflation in the f(T)f(T)-Cosmology

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by $f(T)$ gravity. We show how the torsion contribution to the FRW cosmology can provide a \textit{unique} origin for both early and late acceleration phases of the Universe. The three models ($k=0, \pm 1$) show a \textit{built-in} inflationary behavior at some early Universe time; they restore suitable conditions for the hot big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar $T$ to be a constant function at all time $t$, for the three models. This eliminates the need for the dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models \textit{violate} the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.Comment: LaTeX2e: 19 pages, 9 figures, 1 table. Version 4 Published versio

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

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

Rotating charged AdS solutions in quadratic f(T)f(T) gravity

We present a class of asymptotically anti-de Sitter charged rotating black hole solutions in $f(T)$ gravity in $N$-dimensions, where $f(T)=T+\alpha T^{2}$. These solutions are nontrivial extensions of the solutions presented in \cite{Lemos:1994xp} and \cite{Awad:2002cz} in the context of general relativity. They are characterized by cylindrical, toroidal or flat horizons, depending on global identifications. The static charged black hole configurations obtained in \cite{Awad:2017tyz} are recovered as special cases when the rotation parameters vanish. Similar to \cite{Awad:2017tyz} the static black holes solutions have two different electric multipole terms in the potential with related moments. Furthermore, these solutions have milder singularities compared to their general relativity counterparts. Using the conserved charges expressions obtained in \cite{Ulhoa:2013gca} and \cite{Maluf:2008ug} we calculate the total mass/energy and the angular momentum of these solutions.Comment: 11 pages, Version accepted in EPJ