Zoology of graviton non-Gaussianities during inflation

I discuss graviton non-Gaussianities in models of inflation where de Sitter isometries are spontaneously broken. First, I review the different symmetry breaking patterns following Nicolis, Penco, Piazza, Rattazzi (2015), and discuss which of them can sustain a period of quasi de Sitter expansion. I then show that the symmetry breaking pattern of Solid Inflation captures all the allowed graviton interactions. I conclude by looking at the phenomenological consequences of some of these interactions, and briefly comment on the relation with recently-developed variants of the cosmological bootstrap approach that do not assume linear realization of de Sitter isometries.