  We propose a new class of accelerating world models unifying the cosmological
dark sector (dark matter and dark energy). All the models are described by a
simplified version of the Chaplygin gas Quartessence cosmology. It is found
that even for $\Omega_k \neq 0$, this Quartessence scenario depends only on a
pair of parameters which can severely be constrained by the cosmological tests.
As an example we perform a joint analysis involving the latest SNe type Ia data
and the recent Sloan Digital Sky Survey measurement of baryon acoustic
oscillations. In our analysis we have considered the SNe type Ia Union sample
compiled by Kowalski et al. (2008). At 95.4% (c.l.), we find for BAO + Union
sample, $\alpha=0.81^{+0.04}_{-0.04}$ and $\Omega_{\rm
Q4}=1.15^{+0.16}_{-0.17}$. The best fit for this simplified Quartessence
scenario is a spatially closed Universe and its reduced $\chi^2$ is exactly the
same of the flat concordance model (LambdaCDM)
