Confronting cold new early dark energy and its equation of state with updated CMB, supernovae, and BAO data

Cold new early dark energy (cold NEDE) addresses the Hubble tension through a triggered vacuum phase transition in the dark sector. In this paper, we constrain a phenomenological fluid model using recent cosmic microwave background likelihoods based on Planck NPIPE data alongside baryonic acoustic oscillations (BAO) and supernovae data from Pantheon+. Exploiting the enhanced constraining power of the datasets, we introduce and study an extended version of the NEDE fluid model in which the equation of state parameter wNEDE, characterizing the fluid after the phase transition, is allowed to evolve with nonvanishing derivatives dwNEDE/dlna and d2wNEDE/d(lna)2. Our results indicate that data is compatible with a rather simple time dependence that could arise from a mixture of radiation and a stiff fluid. With the updated datasets, the base and extended models still show a significant reduction of the difference of the maximum tension from 6.3σ in ΛCDM down to 3.5σ with a small simultaneous reduction of the S8 tension, slightly improving over recent findings for the axionlike early dark energy model. Finally, we also provide a first test of the model against new BAO data from the dark energy spectroscopic instrument survey. Replacing the previous BAO constraints in our analysis with the new ones, the tension is further reduced to 2.6σ, reaffirming the cold NEDE model as a promising solution to the Hubble tension.