When Dark Matter Heats Up: A Model-Independent Search for Non-Cold Behavior

TL;DR

This work tests whether dark matter can possess a nonzero or evolving equation of state by performing non-parametric and parametric reconstructions of $w_{ m DM}(z)$ using Gaussian Process Regression on Cosmic Chronometers, Pantheon+, and DESI BAO data. By deriving $w_{ m DM}$ from $E(z)$ and $D(z)$ reconstructed from observations, the authors show that a standard cold DM case $w_{ m DM}=0$ remains broadly consistent, but BAO priors on the sound horizon $r_d$ and the kernel choice can induce mild deviations or sign changes in $w_{ m DM}(z)$ at various epochs. The parametric approach, while offering model comparison via Bayesian evidence, generally disfavors substantial departures from $\,\Lambda$CDM, though DESI data can mimic DM-dynamics when the DE sector is fixed. Overall, the results highlight dataset- and prior-dependent tensions that influence inferred DM properties and motivate tighter, model-independent probes of the dark sector with upcoming surveys.

Abstract

This article questions the common assumption of cold dark matter (DM) by exploring the possibility of a non-zero equation of state (EoS) without relying on any parametric approach. In standard cosmological analyses, DM is typically modeled as pressureless dust with $w_{\rm DM} = 0$, an assumption that aligns with large-scale structure formation, supports the empirical success of the $Λ$CDM model, and simplifies cosmological modeling. However, there is no fundamental reason to exclude a non-zero $w_{\rm DM}$ from the cosmological framework. In this work, we explore this possibility through non-parametric and parametric reconstructions based on Gaussian Process Regression. The reconstructions use Hubble parameter measurements from Cosmic Chronometers (CC), the Pantheon+ sample of Type Ia supernovae, and Baryon Acoustic Oscillation (BAO) data from DESI DR1 and DR2. Our findings suggest that a dynamical EoS for DM, although only mildly supported statistically, cannot be conclusively ruled out. Notably, we observe a mild tendency ($\sim 1σ$) toward a negative $w_{\rm DM}$ at the present epoch, which is most likely due to inconsistencies between the BAO data from DESI and other datasets.

Figures (8)

• Figure 1: Reconstruction of $H(z)$ (upper panel) and $H'(z)$ (lower panel) using 31 CC data points with the squared exponential kernel of the Gaussian approach. The dotted curve in each panel represents the mean of the corresponding reconstructed quantity.
• Figure 2: Reconstruction of $w_{\rm DM} (z)$ using the squared exponential kernel of the Gaussian approach, under the minimal assumption that DE corresponds to the cosmological constant, i.e., $w_{\rm DE} = -1$, for the CC, Pantheon+, CC+Pantheon+, DESI+Pantheon+, and CC+DESI+Pantheon+ datasets. The red dashed curve represents the mean curve of the reconstructed $w_{\rm DM} (z)$, while the solid horizontal line corresponds to $w_{\rm DM} (z) = 0$.
• Figure 3: Whisker plot showing the 68% CL constraints on the present-day value of $w_{\rm DM}(z)$, i.e., $w_{\rm DM}(z = 0)$, for different discrete values of $r_{\rm d}$ (in Mpc) within the interval $135~\mathrm{Mpc} \leq r_{\rm d} \leq 153~\mathrm{Mpc}$, obtained using the squared exponential kernel of the Gaussian process and two combined datasets: CC+DESI-DR2+Pantheon+ (upper panel) and CC+DESI-DR1+Pantheon+ (lower panel).
• Figure 4: Deviation of $w_{\rm DM}(z)$ from zero, quantified by $\Delta w_{\rm DM} = |w_{\rm DM}(z) - 0| / |\sigma_{w_{\rm DM}(z)}|$, for different datasets across various kernels. For the datasets where DESI DR2 BAO is included, the solid red line corresponds to $r_{\rm d} = 149.3 \pm 2.7$ Mpc, while the dashed blue line corresponds to $r_{\rm d} = 137 \pm 3.6$ Mpc. Non-zero evidence for $w_{\rm DM}(z)$ across the redshift range is observed, regardless of the choice of kernel.
• Figure 5: Parametric reconstructions of $w_{\rm DM}$ using different datasets, considering the binned Gaussian approach. These plots represent the functional posterior and were generated using the publicly available Python library fgivenxhandley2019fgivenx. The red dotted curve represents the best-fit curve for each case and the horizontal dotted line corresponds to $w_{\rm DM} =0$.