$\beta$-exponential inflation
  An inflationary scenario driven by a slow rolling homogeneous scalar field whose potential $V(\Phi)$ is given by a generalized exponential function is discussed. Within the {\sl slow-roll} approximation we investigate some of the main predictions of the model and compare them with current data from Cosmic Microwave Background and Large-Scale Structure observations. In particular, we show that this single scalar field model admits a wider range of solutions than do conventional exponential scenarios and predicts acceptable values of the scalar spectral index and of the tensor-to-scalar ratio for the remaining number of {\sl e-folds} lying in the interval $N = 54 \pm 7$ and energy scales of the order of Planck scale. The running of the spectral index is briefly discussed to show that both negative and positive values are predicted by the model here proposed. 
J.S. Alcaniz, F.C. Carvalho (Observatorio Nacional)