Systematics of Adiabatic Modes: Flat Universes
  Adiabatic modes are cosmological perturbations that are locally
indistinguishable from a (large) change of coordinates. At the classical level,
they provide model independent solutions. At the quantum level, they lead to
soft theorems for cosmological correlators. We present a systematic derivation
of adiabatic modes in spatially-flat cosmological backgrounds with
asymptotically-perfect fluids. We find several new adiabatic modes including
vector, time-dependent tensor and time-dependent scalar modes. The new vector
and tensor modes decay with time in standard cosmologies but are the leading
modes in contracting universes. We present a preliminary derivation of the
related soft theorems. In passing, we discuss a distinction between classical
and quantum adiabatic modes, we clarify the subtle nature of Weinberg second
adiabatic mode and point out that the adiabatic nature of a perturbation is a
gauge dependent statement.
