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

Abstract

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