  Consistency relations -- which relate an N-point function to a squeezed
(N+1)-point function -- are useful in large scale structure (LSS) because of
their non-perturbative nature: they hold even if the N-point function is deep
in the nonlinear regime, and even if they involve astrophysically messy galaxy
observables. The non-perturbative nature of the consistency relations is
guaranteed by the fact that they are symmetry statements, in which the velocity
plays the role of the soft pion. In this paper, we address two issues: (1) how
to derive the relations systematically using the residual coordinate freedom in
the Newtonian gauge, and relate them to known results in $\zeta$-gauge (often
used in studies of inflation); (2) under what conditions the consistency
relations are violated. In the non-relativistic limit, our derivation
reproduces the Newtonian consistency relation discovered by Kehagias \& Riotto
and Peloso & Pietroni. More generally, there is an infinite set of consistency
relations, as is known in $\zeta$-gauge. There is a one-to-one correspondence
between symmetries in the two gauges; in particular, the Newtonian consistency
relation follows from the dilation and special conformal symmetries in
$\zeta$-gauge. We probe the robustness of the consistency relations by studying
models of galaxy dynamics and biasing. We give a systematic list of conditions
under which the consistency relations are violated; violations occur if the
galaxy bias is non-local in an infrared divergent way. We emphasize the
relevance of the adiabatic mode condition, as distinct from symmetry
considerations. As a by-product of our investigation, we discuss a simple fluid
Lagrangian for LSS.
