Probing Non-Cold Dark Matter with Modified Emergent Dark Energy
In the standard $Λ$CDM cosmology, dark matter is assumed to be a pressureless cold fluid with $w_{\rm dm}=0$. However, the microscopic nature of dark matter remains unknown, and whether its equation-of-state parameter strictly vanishes deserves observational scrutiny. In this work, we introduce a free dark matter equation-of-state parameter $w_{\rm dm}$ within the Modified Emergent Dark Energy (MEDE) framework, constructing the MEDE+$w_{\rm dm}$ model. We systematically derive its background evolution and linear perturbation equations, and constrain the model parameters using Planck 2018 cosmic microwave background (CMB), DESI DR2 baryon acoustic oscillation (BAO), and three independent Type Ia supernova datasets: Pantheon+, Union3, and DES5YR. Using the CMB + BAO + DES5YR combination, we find a preference for a positive dark matter equation of state, $w_{\rm dm}=0.00128\pm0.00044$, together with a 3$σ$ level preference for quintessence-like dark energy evolution, $α=-0.66\pm0.22$. When the local $H_0$ prior is included, the constraint on $w_{\rm dm}$ remains essentially unchanged, whereas $α$ shifts toward the $Λ$CDM limit, yielding $α=-0.18\pm0.18$. Bayesian model comparison favors $Λ$CDM over MEDE+$w_{\rm dm}$, although the preference is reduced to the weak level after including the local $H_0$ prior. Overall, current observations exhibit a $2.6σ$--$3σ$ preference for a nonzero $w_{\rm dm}$ at the parameter-posterior level, but this indication does not yet constitute a robust detection of non-cold dark matter.