Reviving sub-keV warm dark matter: a UVLF-based analysis

TL;DR

This paper investigates whether sub-keV thermal warm dark matter (WDM) can remain viable if a small cold dark matter (CDM) component carries blue-tilted isocurvature fluctuations that compensate the WDM-induced small-scale power suppression. By constructing a mixed WCDM+CDI model and performing Bayesian inference with a joint data set that includes ultraviolet luminosity functions from HST and JWST, plus CMB, BAO, and SNe, the authors quantify how much the WDM mass bound can loosen when CDI freedom is allowed. They find that, for a pure WDM model, the 95% credible lower bound is $m_{ m WDM}>1.8$ keV, but with CDI at $f_{ m CDM}=0.01$ this relaxes dramatically to $m_{ m WDM}>0.27$ keV, revealing a shallow degeneracy in which blue-tilted CDI partially offsets WDM suppression. The results underscore the potential degeneracy between small-scale physics and initial-condition perturbations, and they motivate combining multiple small-scale probes (e.g., Lyman-$\alpha$, strong lensing, MW satellites, 21-cm) to decisively test compensated WDM scenarios in the future.

Abstract

Thermal warm dark matter (WDM) particles with $m_{\rm WDM} \leq 1~\mathrm{keV}$ are ruled out at more than $4σ$ by multiple observational probes, owing to the strong suppression of small-scale structure induced by early-time free-streaming. Recently, it was highlighted that a small admixture of $\sim1\%$ ($f_{\rm CDM} \sim\!0.01$) cold dark matter (CDM) endowed with a blue-tilted isocurvature spectrum could offset the WDM-induced suppression and relax the WDM mass bound by a factor of $\mathcal{O}(10)$. If viable, this ''warm + cold-isocurvature'' scenario would allow sub-keV WDM particles to constitute nearly the full dark matter abundance while potentially alleviating some small-scale tensions. In this work, we test this mechanism by constraining the WDM mass $m_{\rm WDM}$ while marginalizing over CDM isocurvature parameters. We combine ultraviolet luminosity function measurements from the \textit{Hubble Space Telescope} and \textit{James Webb Space Telescope} over redshift $4 \leq z \leq 11$ with CMB, BAO, and SNe data. For a pure WDM model, our joint analysis yields a lower bound $m_{\rm WDM} > 1.8~\mathrm{keV}$ (95% credible intervals). When CDM isocurvature is introduced at $f_{\rm CDM} = 0.01$, the limit relaxes to $m_{\rm WDM} > 0.27~\mathrm{keV}$ (95% credible intervals), reflecting a shallow degeneracy in which blue-tilted isocurvature fluctuations partially compensate for WDM suppression. These results provide new constraints on thermal WDM in the presence of CDM isocurvature fluctuations and quantify the extent to which such fluctuations can mask the small-scale signatures of light relics.

Figures (7)

• Figure 1: Left: Linear matter transfer functions at $z=0$ from CLASSBlas:2011rf for a WDM model with $m_{\rm WDM}=1~{\rm keV}$, $f_{\rm WDM}=0.99$ and three WCDM models with mixed adiabatic+CDI initial conditions ($f_{\rm iso}=0.293$, $n_{\rm cdi}=2.69,\,2.83,\,2.97$; green dotted, orange solid, blue dot-dashed). The red dashed curve shows the corresponding pure WDM adiabatic case, illustrating how a blue-tilted CDI component can partially offset WDM small-scale suppression. Right: Representative UVLF curves at $z=6$ for the four cosmological models whose transfer functions are shown on the left.
• Figure 2: Plot of matter transfer function $T^{\rm IC}_{\rm X}(k)$ for models $\rm X$ with initial conditions $\rm IC$, as summarized in Tab. \ref{['tab:model_summary']}. The solid blue curve shows a pure WDM model with particle mass $3 \,\mathrm{keV}$ and adiabatic initial conditions. The other curves correspond to WCDM+CDI models, where both WDM and CDM particles are present, with the CDM component carrying additional isocurvature fluctuations.
• Figure 3: Halo mass functions (denoted as $\tilde{n}(M)$) for the six cosmological models at redshifts of $z=4.0$ (in blue), $z=6$ (in red), $z=8$ (in green) and $z=10$ (in yellow), across mass-range from $10^{9}\,\text{--}\,10^{13}~M_\odot$. The square markers denote the $N$-body result using FoF algorithm, while the solid curves represent the theoretical predictions using the excursion-set theory. The WDM masses, $f_{\rm WDM}$ and the initial conditions for the various models are listed in Tab. \ref{['tab:model_summary']}. The analytical ST expression reproduces the simulation results to within $\sim 20\%$ accuracy across nearly all models and redshifts considered.
• Figure 4: Profile likelihood for the WCDM and WCDM+CDI models, constrained using the CMB+BAO+SNe+UVLF likelihoods. The inclusion of CDM isocurvature fluctuations noticeably extends the allowed low-mass region of the WDM parameter space, flattening the profile likelihood down to masses as low as $200\,\mathrm{eV}$ and thereby weakening the lower bound on the WDM mass.
• Figure 5: One- and two-dimensional marginalized posterior distributions for the baseline WCDM and WCDM+CDI models, constrained using the CMB+BAO+SNe+UVLF likelihoods. The inclusion of CDM isocurvature fluctuations primarily broadens the 2$\sigma$ contour toward lower WDM masses, effectively compensating for the small-scale suppression induced by WDM and thereby extending the allowed parameter space. We also include an approximate principal degeneracy direction between $n_{\rm cdi}$ and $m_{\rm WDM}^{-1}$ as a dashed orange curve using Eq. (\ref{['eq:ncdi_final']}).