Examining a new form of non-standard dark matter using DESI DR2 data

In this work, we propose a non-standard dark matter (NSDM) model in which the equation of state (EoS) of dark matter (DM) is parameterized as $w_{\rm dm} = w_2 a^2$, and this DM model is motivated by the idea that DM must become cold dark matter (CDM) in the neighborhood of the scale factor $a = 0$, which implies that both the EoS of DM, $w_{\rm dm}$, and its derivative with respect to the scale factor, ${\rm d}w_{\rm dm}/{\rm d}a$, vanish at $a = 0$. By incorporating the latest cosmological datasets -- including the Planck2018 Cosmic Microwave Background (CMB) distance priors, the Baryon Acoustic Oscillation measurements from the Data Release 2 of the Dark Energy Spectroscopic Instrument (DESI), together with three independent Type Ia Supernova datasets, namely the Dark Energy Survey Year 5 (DESY5) compilation, the Union3 compilation, and the PantheonPlus sample -- we constrain the $\Lambda w_2$DM, $ww_2$DM, and $w_0w_aw_2$DM models, which are constructed by replacing CDM with NSDM in the $\Lambda$CDM, $w$CDM, and $w_0w_a$CDM models, respectively. We find that there is a preference for a negative DM EoS at more than the $3\sigma$ confidence level for the data combinations CMB+DESI+Union3 and CMB+DESI+DESY5. Moreover, for all data combinations, replacing CDM with NSDM in the $w$CDM and $w_0w_a$CDM models significantly reduces the probability of violating the null energy condition. Furthermore, both $ww_2$DM and $w_0w_aw_2$DM are favored over $\Lambda$CDM with a significance comparable to that of the $w_0w_a$CDM model.