  We propose a fully nonlinear framework to construct consistency relations for
testing generic cosmological scenarios using the evolution of large scale
structure. It is based on the covariant approach in combination with a frame
that is purely given by the metric, the normal frame. As an example, we apply
this framework to the LambdaCDM model, by extending the usual first order
conditions on the metric potentials to second order, where the two potentials
start to differ from each other. We argue that working in the normal frame is
not only a practical choice but also helps with the physical interpretation of
nonlinear dynamics. In this frame, effective pressures and anisotropic stresses
appear at second order in perturbation theory, even for "pressureless" dust. We
quantify their effect and compare them, for illustration, to the pressure of a
generic clustering dark energy uid and the anisotropic stress in the DGP model.
Besides, we also discuss the effect of a mismatch of the potentials on the
determination of galaxy bias.
