Generalized inflation in the context of $κ$-deformed theories

Abstract

A new inflationary scenario driven by a slowly-rolling homogeneous scalar field whose potential $V\left(\varphi\right)$ is given by a generalized exponential function is investigated. Within the {\it slow-roll} approximation we obtain the main predictions of the model and compare them with current data from cosmic microwave background and large-scale structure observations. We show that this single scalar field model admits a wider set of solutions than usual exponential scenarios and predicts acceptable values of the spectral index, running of the spectral index and tensor-to-scalar ratio for the remaining number of {\it e}-folds lying in the interval $N = 55 \pm 5$ and an energy scale on which $\lambda \geq \sqrt{2}$; in particular, we observe that the value of the model parameter $\kappa$ depends on the analysis. Finally, the primordial local non-Gaussianity is briefly discussed where we conclude that $k\gtrsim 0.02$ for $f_\text{NL}^\text{local} \ll 1$.