  We reconsider the derivation of soft theorems associated with
nonlinearly-realized symmetries in cosmology. Utilizing the path integral, we
derive a generalized consistency relation that relates a squeezed $(N+1)$-point
correlation function to an $N$-point function, where the relevant soft mode is
at early rather than late time. This generalized (early-late-time) version has
wider applicability than the standard consistency relation where all modes are
evaluated at late times. We elucidate the conditions under which the latter
follows from the former. A key ingredient is the physical mode condition: that
the nonlinear part of the symmetry transformation must match the time
dependence of the dominant, long wavelength physical mode. This is closely
related to, but distinct from, the adiabatic mode condition. Our derivation
sheds light on a number of otherwise puzzling features of the standard
consistency relation: (1) the underlying nonlinearly-realized symmetries (such
as dilation and special conformal transformation SCT) originate as residual
gauge redundancies, yet the consistency relation has physical content---for
instance, it can be violated; (2) the standard consistency relation is known to
fail in ultra-slow-roll inflation, but since dilation and SCT remain good
symmetries, there should be a replacement for the standard relation; (3) in
large scale structure applications, it is known that the standard consistency
relation breaks down if the long wavelength power spectrum is too blue. The
early-late-time consistency relation helps address these puzzles. We introduce
a toy model where explicit checks of this generalized consistency relation are
simple to carry out. Our methodology can be adapted to cases where violations
of the standard consistency relation involve additional light degrees of
freedom beyond the inflaton.
