Ward identities and consistency relations for the large scale structure with multiple species

We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in [1, 2] in the single species case. The multi-species relations apply to the standard dark matter + baryons scenario, as well as to the case in which some of the fields are auxiliary quantities describing a particular population, such as dark matter halos or a specific galaxy class. If a large scale velocity bias exists between the different populations new terms appear in the consistency relations with respect to the single species case. As an illustration, we discuss two physical cases in which such a velocity bias can exist: (1) a new long range scalar force in the dark matter sector (resulting in a violation of the equivalence principle in the dark matter-baryon system), and (2) the distribution of dark matter halos relative to that of the underlying dark matter field.