Inflation and Conformal Invariance: The Perspective from Radial
  Quantization
  According to the dS/CFT correspondence, correlators of fields generated
during a primordial de Sitter phase are constrained by three-dimensional
conformal invariance. Using the properties of radially quantized conformal
field theories and the operator-state correspondence, we glean information on
some points. The Higuchi bound on the masses of spin-s states in de Sitter is a
direct consequence of reflection positivity in radially quantized CFT$_3$ and
the fact that scaling dimensions of operators are energies of states. The
partial massless states appearing in de Sitter correspond from the boundary
CFT$_3$ perspective to boundary states with highest weight for the conformal
group. We discuss inflationary consistency relations and the role of asymptotic
symmetries which transform asymptotic vacua to new physically inequivalent
vacua by generating long perturbation modes. We show that on the CFT$_3$ side,
asymptotic symmetries have a nice quantum mechanics interpretation. For
instance, acting with the asymptotic dilation symmetry corresponds to evolving
states forward (or backward) in "time" and the charge generating the asymptotic
symmetry transformation is the Hamiltonian itself. Finally, we investigate the
symmetries of anisotropic inflation and show that correlators of
four-dimensional free scalar fields can be reproduced in the dual picture by
considering an isotropic three-dimensional boundary enjoying dilation symmetry,
but with a nonvanishing vacuum expectation value of the boundary stress-energy
momentum tensor.
