Consistency Relations of the Large-scale Structure

Consistency relations involving the soft limit of the (n+1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of motion describing the dark matter and galaxy fluids coupled through gravity. We give a summary of the state of the field as well as our latest findings, in particular the implications of the consistency relations for the non-local bias model, halo model and modified gravity.