A minimal model of inflation and dark radiation

We show that a minimal extension of the Standard Model including a new complex scalar field can explain inflation and the observed effective number of neutrinos. The real part of the singlet plays the role of the inflaton field, while the Goldstone boson emerging from the spontaneous symmetry breaking of a global $U(1)$ symmetry contributes to dark radiation and increases the effective number of neutrino species by $0.3$ over the Standard Model value. After detailing the phenomenology of the model, we find that the predicted inflationary observables are in agreement with the current bounds, once the dark radiation component is allowed, both within the metric and Palatini formulation of non-minimally coupled gravity.