Abstract

During inflation, time translations are spontaneously broken by the time-dependent matter field. As a result, the conformal symmetries of de Sitter are spontaneously broken and curvature perturbations can be identified with the ``Goldstone boson’’ associated with this symmetry breaking. Taking this point of view, I will explain how the low-momentum physics of curvature perturbations are constrained by symmetries. I will focus the discussion on two aspects. First, I will show how symmetries force curvature perturbations to freeze on super-horizon scales at all orders in a loop expansion. I will then explain how soft limits of inflationary correlation functions can be derived in a model-independent way using Ward identities. In particular, this approach makes manifest how these soft limits are sensitive to the number of light particles during inflation.