Primordial gravitational waves in supersolid inflation

Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparametrization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate concrete realizations of such a scenario, including non-minimal couplings between gravity and the fields driving inflation. We focus in particular on the dynamics of primordial gravitational waves and discuss how their properties depend on the pattern of symmetry breaking that we consider. Tensor modes can have a blue spectrum, and for the first time we build models in which the squeezed limit of primordial tensor bispectra can be parametrically enhanced with respect to standard single-field scenarios. At leading order in a perturbative expansion, the tensor-to-scalar ratio depends only on the parameter controlling the breaking of space reparametrization. It is independent from the quantities controlling the breaking of time reparametrization, and this represents a difference with respect to standard single-field inflationary models.