Inflationary cosmology in unimodular $F(T)$ gravity

TL;DR

This paper explores how unimodular $F(T)$ gravity can model inflation, reconstructing specific forms of $F(T)$ to match observed cosmic inflation parameters and ensuring a graceful exit from inflation.

Contribution

It develops a reconstruction method for $F(T)$ gravity under unimodular conditions and applies it to various inflationary scenarios consistent with observational data.

Findings

Predictions align with Planck data for multiple inflation models

The framework allows for a graceful exit in inflation

Reconstruction procedure is versatile for different scale-factor evolutions

Abstract

We investigate the inflationary realization in the context of unimodular $F(T)$ gravity, which is based on the $F(T)$ modification of teleparallel gravity, in which one imposes the unimodular condition through the use of Lagrange multipliers. We develop the general reconstruction procedure of the $F(T)$ form that can give rise to a given scale-factor evolution, and then we apply it in the inflationary regime. We extract the Hubble slow-roll parameters that allow us to calculate various inflation-related observables, such as the scalar spectral index and its running, the tensor-to-scalar ratio, and the tensor spectral index. Then, we examine the particular cases of de Sitter and power-law inflation, of Starobinsky inflation, as well as inflation in a specific model of unimodular $F(T)$ gravity. As we show, in all cases the predictions of our scenarios are in a very good agreement with Planck observational data. Finally, inflation in unimodular $F(T)$ gravity has the additional advantage that it always allows for a graceful exit for specific regions of the model parameters.