Observational constraints on noncold dark matter and phenomenological emergent dark energy

It is well known that there are several long-standing problems implying the discordance of the $\Lambda$CDM model. Although most of the models proposed to resolve these problems assume that dark matter is pressureless, it is still possible that dark matter is not cold, as current observations have not ruled out this possibility yet. Therefore, in this article, we treat the dark matter equation of state parameter as a free parameter, and apply observational data to investigate the non-coldness of dark matter. Impressing by the simplicity of the phenomenological emergent dark energy (PEDE) and its ability to relieve the Hubble tension, we propose the PEDE+$w_{\rm dm}$ model based on PEDE and non-cold dark matter. We then place constraints on this model in light of the Planck 2018 Cosmic Microwave Background (CMB) anisotropies, baryon acoustic oscillation (BAO) measurements, and the Pantheon compilation of Type Ia supernovae. The results indicate a preference for a negative dark matter equation of state parameter at $95\%$ CL for all data sets except CMB alone and CMB+BAO, which suggests that the non-coldness assumption of dark matter worth to be investigated further in order to understand the nature of dark matter. The Hubble tension is alleviated in this scenario compared to the $\Lambda$CDM model, with a significance below 3$\sigma$ level for all data sets except CMB+Pantheon. However, from the analysis based on Bayesian evidence, we clearly see that the data sets favor $\Lambda$CDM over the PEDE+$w_{\rm dm}$ model.