Probing the sound speed and clustering of dark energy

Recent Dark Energy Spectroscopic Instrument (DESI) observations favor a dynamical dark energy component with a time-varying equation-of-state, potentially crossing the cosmological-constant boundary \(w=-1\), challenging the standard \(\Lambda\)CDM paradigm. In this paper we present the first joint observational constraints on the clustering properties of such dynamical dark energy, using both the Parameterized Post-Friedmann (PPF) framework and the effective field theory (EFT) of dark energy. Combining DESI DR2 baryon acoustic oscillations with Planck 2018 cosmic microwave background data and the Union3 supernova sample, we constrain the effective sound speed \(c_s^{2}\). For a time-varying equation-of-state, the degeneracy between \((1+w)\) and \(c_s^{2}\) is broken, yielding the first meaningful constraint \(\log_{10}c_{s}^{2}=-3.00^{+2.9}_{-0.99}\), while constant-\(w\) models remain unconstrained. A complementary EFT analysis gives consistent results, favoring \(c_s^{2}\sim 0.3\) or \(0.4\). Our findings demonstrate that current data are now sensitive to the perturbative properties of dynamical dark energy, opening a new observational window on the nature of cosmic acceleration.