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

TL;DR

This paper explores a specific class of $f(T)$ gravity theories in a flat universe, showing they can naturally produce Starobinsky-like inflation models with unique predictions for inflationary parameters.

Contribution

It introduces a special class of $f(T)$ gravity in a flat universe that naturally yields Starobinsky-like inflation without conformal transformations.

Findings

The $f(T)$ gravity model is consistent with inflationary scenarios.

The model predicts double solutions for tensor-to-scalar ratios at a given spectral index.

The potential interpolates between Starobinsky and quadratic inflation models.

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.