Reconciling tensor and scalar observables in G-inflation

Abstract

The simple m2ϕ2 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 ns. 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 αs that can be of order ns−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 |αs| place a lower bound of r≳ 0.005 and, conversely, a given r places a lower bound on |αs|, both of which are potentially observable with next generation CMB and large scale structure surveys.