Reconciling tensor and scalar observables in G-inflation

The simple m^2phi2 potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio r and measurements of the scalar spectral index n_s. Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll approximation leading to a relatively large and negative running of the tilt α_s that can be of order n_s-1. We show that the observables on CMB and large scale structure scales can be predicted accurately using the optimized slow-roll approach instead of the traditional slow-roll expansion. Upper limits on |α_s| place a lower bound of rgtrsim 0.005 and, conversely, a given r places a lower bound on |α_s|, both of which are potentially observable with next generation CMB and large scale structure surveys.