Reconstructing inflation in scalar-torsion $f(T,\phi)$ gravity

TL;DR

This paper develops a reconstruction method for scalar-torsion $f(T,)$ gravity during slow-roll inflation, linking observable inflationary parameters to the functions defining the theory, and analyzes specific attractor scenarios.

Contribution

It introduces a novel reconstruction scheme for scalar-torsion theories based on inflationary observables, providing explicit forms of coupling and potential functions for different attractors.

Findings

Derived explicit forms of $F()$ and $V()$ for various attractors.

Established constraints on model parameters from inflationary data.

Analyzed specific attractor cases like $n_s-1 \\propto 1/N$ and $r \\propto 1/N$.

Abstract

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function $f(T,\phi)$ of the torsion scalar $T$ of teleparallel gravity and the inflaton $\phi$. For the class of theories with Lagrangian density $f(T,\phi)=-M_{pl}^{2} T/2 - G(T) F(\phi) - V(\phi)$, with $G(T)\sim T^{s+1}$ and the power $s$ as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function $F(\phi)$ and the scalar potential $V(\phi)$ through the parametrization (or attractor) of the scalar spectral index $n_{s}(N)$ and the tensor-to-scalar ratio $r(N)$ as functions of the number of $e-$folds $N$. As specific examples, we analyze the attractors $n_{s}-1 \propto 1/N$ and $r\propto 1/N$, as well as the case $r\propto 1/N (N+\gamma)$ with $\gamma$ a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function $F(\phi)$ and the potential $V(\phi)$, as also the constraints on the parameters present in our model and its reconstruction.