Single-Field Consistency Relations of Large Scale Structure
  We derive consistency relations for the late universe (CDM and \Lambda CDM):
relations between an n-point function of the density contrast \delta and an
(n+1)-point function in the limit in which one of the (n+1) momenta becomes
much smaller than the others. These are based on the observation that a long
mode, in single-field models of inflation, reduces to a diffeomorphism since
its freezing during inflation all the way until the late universe, even when
the long mode is inside the horizon (but out of the sound horizon). These
results are derived in Newtonian gauge, at first and second order in the small
momentum q of the long mode and they are valid non-perturbatively in the
short-scale \delta. In the non-relativistic limit our results match with
(Kehagias and Riotto '13) and (Peloso and Pietroni '13). These relations are a
consequence of diffeomorphism invariance; they are not satisfied in the
presence of extra degrees of freedom during inflation or violation of the
Equivalence Principle (extra forces) in the late universe.
