Hints of noncold dark matter? Observational constraints on barotropic dark matter with a constant equation of state parameter

This study investigates the potential of a cosmological model termed $\mathrm{\Lambda }w$DM, in which a cosmological constant play the role of dark energy and dark matter is barotropic and has a constant equation of state parameter ($w_{\mathrm{d}\mathrm{m}}$), to address the $S_8$ tension between early- and late- universe observations. By incorporating the latest cosmological datasets – including Planck Cosmic Microwave Background (CMB), Baryon Acoustic Oscillation (BAO), Ia supernovae (SNe Ia), Redshift Space Distortions (RSD), and weak lensing (WL) – we constrain the $\mathrm{\Lambda }w$DM compared to $\mathrm{\Lambda }$CDM. Our analysis reveals a marginal preference for a non-zero $w_{\mathrm{d}\mathrm{m}}=2.7_{-1.9}^{+2.0}\times {10}^{-7}$( at 95% confidence level) when combining CMB, SDSS BAO, SNe Ia, RSD, and WL data, and a marginal preference for a non-zero $w_{\mathrm{d}\mathrm{m}}=2.29_{-2.0}^{+1.9}\times {10}^{-7}$( at 95% confidence level) when combining CMB, DESI Y1 BAO, SNe Ia, RSD, and WL data. In addition, we find that, compared to $\mathrm{\Lambda }$CDM, $\mathrm{\Lambda }w$DM can alleviate the $S_8$ tension from $>3\sigma$ to $<1\sigma$. Furthermore, we find that, for CMB+SDSS+PP+RSD+WL datasets, the $\mathrm{\Lambda }w$DM model is close to being positively preferred over the $\mathrm{\Lambda }$CDM model.