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

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 $f(T,\varphi )$ of the torsion scalar $T$ of teleparallel gravity and the inflaton $\varphi$. For the class of theories with Lagrangian density $f(T,\varphi )=-M_{pl}^{2}T/2-G(T)F(\varphi )-V(\varphi )$, 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 $F(\varphi )$ and the scalar potential $V(\varphi )$ 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 $F(\varphi )$ and the potential $V(\varphi )$, as also the constraints on the parameters present in our model and its reconstruction.

14 pages, 1 figure, Accepted version for publication in EPJC

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