Observational Viability of an Inflation Model with E-Model non-Minimal Derivative Coupling

Abstract: By starting with a two-fields model in which the fields and their derivatives are nonminimally coupled to gravity, and then by using a conformal gauge, we obtain a model in which the derivatives of the canonically normalized field are nonminimally coupled to gravity. By adopting some appropriate functions, we study two cases with constant and E-model nonminimal derivative coupling, while the potential in both cases is chosen to be E-model one. We show that in contrary to the single field $\alpha$-attractor model that there is an attractor \textit{point} in the large $N$ and small $\alpha$ limits, in our setup and for both mentioned cases there is an attractor \emph{line} in these limits that the $r-n_{s}$ trajectories tend to. By studying the linear and nonlinear perturbations in this setup and comparing the numerical results with Planck2015 observational data, we obtain some constraints on the free parameter $\alpha$. We show that by considering the E-model potential and coupling function, the model is observationally viable for all values of $M$ (mass scale of the model). We use the observational constraints on the tensor-to-scalar ratio and the consistency relation to obtain some constraints on the sound speed of the perturbations in this model. As a result, we show that in a nonminimal derivative $\alpha$-attractor model, it is possible to have small sound speed and therefore large non-Gaussianity.