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.
Scalar-Torsion Theories in Four Dimensional Static Spacetimes
