I will review how the requirements of unitarity, locality, causality and Lorentz invariance impose constraints on the signs of the operator coefficients in an effective field theory, discuss recent work on generalizing these constraints to arbitrary spin particles, and discuss how these can be used to constraint gravitational EFTs of the type considered by cosmologists as models for dark energy or inflation.

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.

To make a robust measurement of the minimal neutrino mass requires an exquisite measurement of the matter power spectrum on small scales. An unbiased measurement of the matter in the Universe can be made through the effect of gravitational lensing. Until recently it was expected that future measurements of the lensing potential (using the CMB and LSS) would be sufficient. Unfortunately, to estimate the neutrino mass from the small scale power spectrum also requires a precise measurement of the intrinsic amplitude of (matter) fluctuations. Although in principle the CMB can be used to make such a measurement, current data is not good enough, because of a degeneracy that exists between the amplitude of fluctuations and the reinization optical depth. In this talk I will explain this problem in some detail and provide several possible solutions. In addition, I will discuss some work in progress on measuring the lensing potential using intensity mapping experiments (i.e. 21cm).