We present a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. Within this model, which we designate as ``Generalized Natural Inflation'', we analyze how the dynamics fundamentally depends on the mass of the radial mode and determine the size of the non-Gaussianities arising from such a scenario.

We also motivate ongoing research within the coset construction formalism, that aims to clarify how the spontaneous symmetry breaking pattern of spacetime, gauge, and internal symmetries may allow us to get a deeper understanding, and an actual algebraic classification in the spirit of the so-called zoology of condensed matter'', of different possible cosmic states'', some of which may be quite relevant for model-independent statements about different phases in the evolution of our universe. The outcome of these investigations will be reported elsewhere.