Clustering in dynamical dark energy: observational constraints from DESI, CMB, and supernovae

We investigate the clustering properties of dynamical dark energy using the latest cosmological observations. We describe the dark energy perturbation within two complementary frameworks, namely the Parameterized Post-Friedmann (PPF) approach and the Effective Field Theory (EFT) of dark energy. Using DESI DR2 baryon acoustic oscillations together with Planck 2018 CMB data and the Union3 supernova sample, we constrain the effective sound speed of dark energy in both the $w$CDM and $w_0w_a$CDM backgrounds. Within the PPF description, the sound speed remains unconstrained for $w$CDM, while for the $w_0w_a$CDM case we obtain $\log_{10} c_s^2 = -3.00^{+2.9}_{-0.99}$. Additionally, in the EFT framework, both models favor a small sound speed, with a mean value $c_s^2 \simeq 0.3$--$0.4$ but with significant uncertainties. For dynamical dark energy, the reconstructed equation of state clearly exhibits a quintom-B behavior, and its deviation from $\Lambda$CDM reaches $3.42\sigma$, rising to $3.63\sigma$ when PPF perturbations are included and reducing to $3.19\sigma$ in the EFT case. Finally, model comparison using information criteria shows that the $w_0w_a$CDM model with a smooth, non-clustering dark energy component ($c_s^2 = 1$) is preferred by AIC, whereas BIC favors $\Lambda$CDM. In summary, current data indicate a mild preference for dynamical dark energy but no evidence for significant clustering, which implies the need for future high-precision observations to probe the perturbative behavior more definitively.