The matter with(in) CPL

We introduce a two-parameter phenomenological extension of the $\Lambda$CDM model in which the equation of state parameter of the ``dust’’ fluid becomes different from zero for redshifts below a transition value $z_t$. Using data from DESI DR2 BAO, DESY5 Sn~Ia and CMB distance priors ($R,l_A,\omega_b$) data, we compare our model with the standard CPL parameterization $w_0-w_a$ for dynamical dark energy. Using the Deviance Information Criteria (DIC), we find that the two models are essentially indistinguishable ($\Delta$DIC $<$ 2) and preferred over $\Lambda$CDM with a significance $\geq 3 \sigma$. We discuss how this parameterization finds a natural interpretation in the context of cosmological backreaction and derive a prediction for the evolution of the growth factor, discussing its impact on low redshift $f\sigma_8$ measurements.