Reconstructing inflation in scalar-torsion $f(T,ϕ)$ 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, φ ) of the torsion scalar T of teleparallel gravity and the inflaton φ . For the class of theories with Lagrangian density, with G(T ) ∼ T s+1 and the power s a constant, we consider a reconstruction scheme for determining both the nonminimal coupling function F(φ ) and the scalar potential V (φ ) 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 ∝ 1/N and r ∝ 1/N, as well as the case r ∝ 1/N(N + γ) with γ a dimensionless constant.

Unified dark sectors in scalar-torsion theories of gravity

“…In this framework one can also introduce scalar fields, i.e. constructing scalar-torsion theories [28], allowing for non-minimal [28][29][30][31][32][33] or derivative [34] couplings with torsion, or more general constructions [35][36][37][38][39][40][41][42][43], than can even be the teleparallel version of Horndeski theories [44][45][46][47].…”