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.