Reconstructing inflation in scalar-torsion $f(T,phi)$ gravity. (arXiv:2106.06145v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Gonzalez_Espinoza_M/0/1/0/all/0/1">Manuel Gonzalez-Espinoza</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Herrera_R/0/1/0/all/0/1">Ramón Herrera</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Otalora_G/0/1/0/all/0/1">Giovanni Otalora</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Saavedra_J/0/1/0/all/0/1">Joel Saavedra</a>
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.
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.
http://arxiv.org/icons/sfx.gif
