The equation of state (EOS) in quartessence models interpolates between two stages: $psimeq 0$ at high energy densities and $papprox -rho$ at small ones. In the quartessence models analyzed up to now, the EOS is convex, implying increasing adiabatic sound speed ($c_{s}^{2}$) as the energy density decreases in an expanding Universe. A non-negligible $c_{s}^{2}$ at recent times is the source of the matter power spectrum problem that plagued all convex (non-silent) quartessence models. Viability for these cosmologies is only possible in the limit of almost perfect mimicry to $Lambda$CDM. In this work we investigate if similarity to $Lambda$CDM is also required in the class of quartessence models whose EOS changes concavity as the Universe evolves. We focus our analysis in the simple case in which the EOS has a step-like shape, such that at very early times $psimeq0$, and at late times $psimeq const<0$. For this class of models a non-negligible $c_{s}^{2}$ is a transient phenomenon, and could be relevant only at a more early epoch. We show that agreement with a large set of cosmological data requires that the transition between these two asymptotic states would have occurred at high redshift ($z_tgtrsim38$). This leads us to conjecture that the cosmic expansion history of any successful non-silent quartessence is (practically) identical to the $Lambda$CDM one.
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