$\Lambda$XCDM: a running vacuum strategy for crossing the phantom divide

Composite dynamical dark energy (DDE) has recently been explored as an efficient way to help cure cosmological tensions through the so-called $w$XCDM model {Gomez-Valent:2024tdb,Gomez-Valent:2024ejh}, a toy-model version of the $\Lambda$XCDM model {Grande:2006nn}. The latter is a composite running vacuum model (RVM) that involves a DE component $X$ (`cosmon') of generic nature. We compute the effective equation of state of $\Lambda$XCDM and use state-of-the-art techniques to fit this model to two standard sets of cosmological data, one involving SNIa from Pantheon$+$ and the other SNIa from DES-Dovekie, in addition to BAO data from DESI DR2 and the CMB data from Planck PR4. We do not use large scale structure formation data for this analysis nor the SH0ES calibration of $H_0$. We find that $\Lambda$XCDM naturally performs the crossing of the phantom divide as observed by DESI near $z\simeq 0.4$ using the $w_0w_a$CDM parameterization, a feature well favored by existing model-agnostic analyzes of the same data {Gonzalez-Fuentes:2025lei,Gonzalez-Fuentes:2026rgu}. It turns out that the cosmon $X$ behaves as `phantom matter' (PM) near the present, which in contrast to usual phantom DE satisfies the strong energy condition (as ordinary matter) and furnishes positive pressure ($P_X>-\rho_X>0$) at the expense of negative energy density ($\rho_X<0$). $\Lambda$XCDM provides a better fit than $w_0w_a$CDM and, as a bonus, alleviates the cosmic coincidence problem. Given that PM appears in stringy versions of the RVM, the $\Lambda$XCDM appears to be a composite DDE model with a good chance of explaining the crossing of the phantom divide from first principles, therefore providing theoretical support to the DESI observations inferred from generic parameterizations of the DE.