Power-law and intermediate inflationary models in f(T)-gravity

TL;DR

This paper explores inflationary models within $f(T)$-gravity, demonstrating that certain power-law and intermediate inflation scenarios can align with observational data, unlike in standard Einstein gravity.

Contribution

It introduces inflationary models in $f(T)$-gravity with power-law forms, showing their compatibility with Planck data and refining inflationary potentials.

Findings

Power-law and intermediate inflation models are compatible with Planck 2015 data in $f(T)$-gravity.

The potentials for these models have power-law forms with different exponents.

The quartic potential $V() o ^4$ can fit observations in $f(T)$-gravity, unlike in standard inflation.

Abstract

We study inflation in the framework of $f(T)$-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in $f(T)$-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law form for the $f(T)$ function in the action and examine the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, in the considered $f(T)$-gravity scenario, the power-law and intermediate inflationary models can be compatible with the observational results of Planck 2015 at 68\% CL. In our $f(T)$-gravity setting, the potentials responsible for both the power-law and intermediate inflationary models have the power-law form $V(\phi ) \propto {\phi ^m}$ but the power $m$ is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of $f(T)$-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, the self-interacting quartic potential $V(\phi ) \propto {\phi ^4}$ which has special reheating properties, can be consistent with the Planck 2015 data in our $f(T)$-gravity scenario while it is ruled out in the standard inflationary scenario.