Degeneracy between warm and coupled cold dark matter: A clarifying note
  Wei et al [PRD 88, 043510 (2013)] have proposed the existence of a
cosmological degeneracy between warm dark matter (WDM), modified gravity and
coupled cold dark matter (CDM) cosmologies at both the background expansion and
the growth of density perturbation levels, i.e., corresponding cosmological
data would not be able to differentiate such scenarios. Here, we will focus on
the specific indistinguishability between a warm dark matter plus cosmological
constant ($\Lambda$) and coupled scalar field-CDM scenarios. Although the
statement of Wei et al is true for very specific conditions we present a more
complete discussion on this issue and show in more detail that these models are
indeed distinguishable. We show that the degeneracy breaks down since coupled
models leave a specific signature in the redshift space distortion data which
is absent in the uncoupled warm dark matter cosmologies. Furthermore, we
complement our claim by providing the reasons which suggest that even at
nonlinear level a breaking of such apparent equivalence is also expected.
