Inflation, Symmetry, and B-Modes
  We examine the role of using symmetry and effective field theory in
inflationary model building. We describe the standard formulation of starting
with an approximate shift symmetry for a scalar field, and then introducing
corrections systematically in order to maintain control over the inflationary
potential. We find that this leads to models in good agreement with recent
data. On the other hand, there are attempts in the literature to deviate from
this paradigm by invoking other symmetries and corrections. In particular: in a
suite of recent papers, several authors have made the claim that standard
Einstein gravity with a cosmological constant and a massless scalar carries
conformal symmetry. They further claim that such a theory carries another
hidden symmetry; a global SO(1,1) symmetry. By deforming around the global
SO(1,1) symmetry, they are able to produce a range of inflationary models with
asymptotically flat potentials, whose flatness is claimed to be protected by
these symmetries. These models tend to give rise to B-modes with small
amplitude. Here we explain that these authors are merely introducing a
redundancy into the description, not an actual conformal symmetry. Furthermore,
we explain that the only real (global) symmetry in these models is not at all
hidden, but is completely manifest when expressed in the Einstein frame; it is
in fact the shift symmetry of a scalar field. When analyzed systematically as
an effective field theory, deformations do not generally produce asymptotically
flat potentials and small B-modes, but other types of potentials with B-modes
of appreciable amplitude. Such simple models typically also produce the
observed red spectral index, Gaussian fluctuations, etc. In short: simple
models of inflation, organized by expanding around a shift symmetry, are in
excellent agreement with recent data.
