From symmetries to cosmological observables

Many models of inflation in field theory require an underlying approximate shift symmetry to drive a prolonged phase of accelerated expansion. In UV-finite theories of gravity such as string theory, the shift symmetry is generically required for successful models. Despite the crucial role it plays, the observable, model independent consequences of a shift symmetry are yet unknown. In this talk, I will derive these consequences for primordial curvature correlators in single clock inflation.
I will discuss the two main paths from symmetry to cosmological observables: Effective Field Theories (EFT) and Ward-Takahashi identities. First, I will derive the restrictions on the well-known EFT of cosmological backgrounds (a.k.a. the EFT of Inflation) implied by a shift symmetry of the clock. The resulting EFT of shift-symmetric cosmologies describes, among other systems, perfect and imperfect superfluids coupled to gravity and driven superfluids in the decoupling limit. Second, I will derive new Ward-Takahashi identities for the squeezed limit of cosmological correlators using the language of adiabatic modes. I will conclude discussing the yet unexplored class of generalized adiabatic modes that arise from mixing spacetime diffeomorphism with internal symmetries.