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 rpropto 1/N, as well as the case rpropto 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.
Highlights
On the other hand, the teleparallel equivalent of General Relativity (GR) or Teleparallel Gravity (TG) is a gauge theory for the translation group which constitutes an alternative description of gravity based on torsion [11,12,13,14,15,16,17,18,19,20,21,22,23]
Since the field strength is just the torsion tensor, it is used to construct a torsion-quadratic scalar dubbed torsion scalar T which becomes the Lagrangian density of TG
TG coincides with the General Relativity (GR) at the level of field equations these non-minimally coupled scalar-torsion theories belong to a different class of gravitational modifications
Summary
The teleparallel equivalent of GR or Teleparallel Gravity (TG) is a gauge theory for the translation group which constitutes an alternative description of gravity based on torsion [11,12,13,14,15,16,17,18,19,20,21,22,23]. In the context of inflation the reconstruction of the background variables (effective potential, coupling functions, scale factor) of the inflationary models, from the observational quantities (the scalar spectrum, scalar spectral index and the tensor-to-scalar ratio) has been studied by different authors, see Refs. In particular we consider the ansatz for the scalar spectral index ns(N ) in both cases in which ns = 1−2/N and for the tensorto-scalar ratio r (N ) we will analyze the cases r (N ) = q/N and r (N ) = q/[N (N + γ )] where q and γ are constants In this respect, we will reconstruct the effective potential V (φ) and the non-minimal coupling parameter F(φ) as a function of the inflaton field φ. Where Sμνρ is the dubbed superpotential which is linear in the torsion tensor [11]
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