On Observables in a Dark Matter-Clustering Quintessence System
  We consider a system where dark matter dynamics is enriched by the presence
of clustering quintessence in the approximation where the system is effectively
reduced to one degree of freedom. We study the corresponding observables up to
one-loop order and then point out similarities between the power spectrum of
the reduced system and the behaviour of non-equal time pure dark matter
correlators. We then focus on the one-loop total density power spectrum in the
IR limit as a diagnostic tool for consistency relations breaking. Unlike the
non-equal time case, the reduced system does still obey consistency relations;
we illustrate this by explicitly verifying the 1-loop IR cancellation. A more
general setup, obtained by relaxing the assumption of a vanishing sound speed,
is also analyzed. In this and similar scenarios the presence of additional
dynamics, typical of dark energy and modified gravity models, implies that one
may no longer gauge away the squeezed contribution of observables such as the
dark matter bispectrum. We show how these effects propagate all the way to
biased tracers.
