Consistency Relations for the Conformal Mechanism
  We systematically derive the consistency relations associated to the
non-linearly realized symmetries of theories with spontaneously broken
conformal symmetry but with a linearly-realized de Sitter subalgebra. These
identities relate (N+1)-point correlation functions with a soft external
Goldstone to N-point functions. These relations have direct implications for
the recently proposed conformal mechanism for generating density perturbations
in the early universe. We study the observational consequences, in particular a
novel one-loop contribution to the four-point function, relevant for the
stochastic scale-dependent bias and CMB mu-distortion.
