On observables in a dark matter-clustering quintessence system

We consider a system where dark matter (DM) dynamics is enriched by the presence of clustering quintessence in the approximation where the system is effectively reduced to one degree of freedom. We focus on the behaviour of the one-loop total density power spectrum in the IR limit and on the so-called consistency conditions (ccs). We find that the power spectrum shows an enhancement in the IR with respect to the pure dark matter case and suggest a parallel with the behaviour of the non-equal time pure (DM) correlator. We then analyze ccs for a more general setup and recover the result that, for cs=w, ccs are conserved outside the horizon but generically not inside. We extend these results. In these and similar scenarios the presence of additional dynamics (e.g. dark energy, modified gravity) implies that one may not "gauge away" the squeezed contribution of observables such as the dark matter bispectrum. We comment on how these effects may propagate all the way to biased tracers observables.