Features and New Physical Scales in Primordial Observables: Theory and
  Observation
  All cosmological observations to date are consistent with adiabatic, Gaussian
and nearly scale invariant initial conditions. These findings provide strong
evidence for a particular symmetry breaking pattern in the very early universe
(with a close to vanishing order parameter, $\epsilon$), widely accepted as
conforming to the predictions of the simplest realizations of the inflationary
paradigm. However, given that our observations are only privy to perturbations,
in inferring something about the background that gave rise to them, it should
be clear that many different underlying constructions project onto the same set
of cosmological observables. Features in the primordial correlation functions,
if present, would offer a unique and discriminating window onto the parent
theory in which the mechanism that generated the initial conditions is
embedded. In certain contexts, simple linear response theory allows us to infer
new characteristic scales from the presence of features that can break the
aforementioned degeneracies among different background models, and in some
cases can even offer a limited spectroscopy of the heavier degrees of freedom
that couple to the inflaton. In this review, we offer a pedagogical survey of
the diverse, theoretically well grounded mechanisms which can imprint features
into primordial correlation functions in addition to reviewing the techniques
one can employ to probe observations. These observations include cosmic
microwave background anisotropies and spectral distortions as well as the
matter two and three point functions as inferred from large-scale structure and
potentially, 21 cm surveys.
