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.
Highlights
The general relativity (GR) theory explained the gravity as spacetime curvature
Instead of restricting ourselves to Spatially flat universe (SFU), we impose flat like universe (FLU) assumptions onto the modified f (T ) Friedmann equations. This model identifies a hidden class of f (T ) gravity theories that cannot be covered by assuming a SFU
Page 5 of 14 279 tions as an input; the scale factor a(t) is obtained as an output. (b) In the f (T ) theories, a fixed equation of state (EoS) parameter in addition to a scale factor a(t) is entered into the Friedmann equations as inputs; an f (T ) is obtained as an output. (c) In this work, which is governed by the f (T ) framework, we introduce two conditions (the FLU model assumptions (15) and (16)) as inputs; we get a scale factor a(t), f (T ), and a dynamical EoS parameter ω(t) as outputs
Summary
The general relativity (GR) theory explained the gravity as spacetime curvature. This description of gravitation has succeeded to confront astrophysical observations for a long time. An interesting variant of the TEGR is the Born–Infeldmodified teleparallel gravity Within this framework the early cosmic acceleration (inflation) could be accounted for with no need of an inflaton field [22,23]. Another remarkable variant of generalizations of TEGR are the f (T ) theories similar to the f (R) extensions of the Einstein–Hilbert action. Instead of restricting ourselves to SFU, we impose FLU assumptions onto the modified f (T ) Friedmann equations This model identifies a hidden class of f (T ) gravity theories that cannot be covered by assuming a SFU.
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