Preprint number: CP3-Origins-2011-45 and DIAS-2011-40
We explore the paradigm according to which inflation is driven by a four-dimensional strongly coupled dynamics coupled non-minimally to gravity. We start by introducing the general setup, both in the metric and Palatini formulation, for generic models of composite inflation. We then analyze the relevant example where the inflaton is identified with the glueball field of a pure Yang-Mills theory. We use the well known dilatonic-like glueball action obtained requiring the saturation, at the effective action level, of the underlying Yang-Mills trace anomaly. We then couple the theory to gravity non-minimally. We demonstrate that it is possible to achieve successful inflation with the confining scale of the underlying Yang-Mills theory naturally of the order of the grand unified energy scale. We also argue that the metric formulation is better suited to investigate models of composite inflation. Finally we show that, in the metric formulation, the model nicely respects tree-level unitarity for the scattering of the inflaton field all the way to the Planck scale.