Slow-roll inflation in generalized scalar-torsion gravity

We study the dynamics of inflation in a generalized scalar-torsion gravity scenario by assuming a canonical scalar field non-minimally coupled to torsion with a Galileon-type self-interaction. After obtaining the field equations for a flat FRW background, we derive the second order action for both scalar and tensor perturbations to compute the power spectra of primordial fluctuations. As particular models, we studied at first, a power-law form of coupling function $F(x)=1+\xi x^{2}/2$, with $x\equiv \phi/M_{pl}$, and a monomial scalar field potential $V(x)=\lambda x^{n}/n$ which is ruled out at $2\sigma$ level by current observational data for $n\geq 2$. Under slow-roll approximation we obtain analytical expressions for the background as well as perturbative dynamics, and we show that the predictions of the model are consistent with current Planck 2018 constraints on the spectral index $n_{s}$ and the tensor-to-scalar ratio $r$ through the $n_s-r$ plane. Accordingly, this model is in agreement with current observational bounds only within the $95\%$ C.L. region in the case of chaotic quadratic inflation ($n=2$), whereas that for the other monomial potentials such as $n=4/3$, $n=1$ and $n=2/3$, it is found that they are even more favoured, overlapping their results with the $68\%$ C.L. region from last Planck data. Secondly, we studied a model in which the presence of both non-minimal coupling to gravity and the Galileon non-linear self-interaction $\gamma (\partial \phi)^2 \Box{\phi}$ leads to a suppression of the tensor-to-scalar ratio compared to those predicted in the standard scenario, then predicting $0.024\lesssim r\lesssim 0.069$. This result allows us to reconcile chaotic quadratic inflation with current Planck data up to the $68\%$ C.L. region.