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

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.

💡 Research Summary

This paper investigates whether sub‑keV thermal warm dark matter (WDM) can remain viable when a tiny fraction of cold dark matter (CDM) carries a blue‑tilted isocurvature perturbation. In the standard picture, thermal WDM particles with masses ≤ 1 keV are excluded at > 4σ by a suite of probes because free‑streaming erases small‑scale density fluctuations. Recent work suggested that adding ≈ 1 % CDM with a strongly blue isocurvature spectrum could partially restore the suppressed power, potentially relaxing the WDM mass bound by an order of magnitude.

The authors embed this “WDM + cold‑isocurvature (CDI)” scenario into a full cosmological inference pipeline. They define the warm fraction f_WDM = Ω_WDM/Ω_DM and the CDM fraction f_CDM = 1 − f_WDM. The isocurvature component is characterized by an amplitude A_iso and a spectral index n_iso, with a pivot k_p = 0.05 Mpc⁻¹. To capture the physical impact of the isocurvature mode they introduce an effective parameter f_iso ≡ (1 − f_WDM) f_cdi, where f_cdi = q A_iso/A_ad and q encodes the CDM density fraction. The total matter transfer function is then a combination of the adiabatic WDM transfer function T_ad WDM(k) and the CDI response R_cdi CDM(k), modulated by f_iso. This formulation makes explicit that the compensation of WDM free‑streaming depends on the product r_c f_cdi ∝ f_iso.

To probe the small‑scale regime where the compensation is most effective, the authors use ultraviolet luminosity function (UVLF) measurements of high‑redshift galaxies from Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) covering 4 ≤ z ≤ 11. The UVLF is linked to the halo mass function (HMF) through a star‑formation efficiency model; a suppression of low‑mass halos caused by WDM translates into a deficit of faint galaxies. By incorporating the HMF modifications induced by both WDM free‑streaming and CDI‑enhanced power, the UVLF becomes a sensitive probe of the combined model.

The analysis combines the UVLF data with large‑scale cosmological observations: Planck 2018 CMB temperature and polarization spectra, BOSS/eBOSS baryon acoustic oscillation (BAO) distance measurements, and the Pantheon Type Ia supernova sample. A Bayesian Markov Chain Monte Carlo (MCMC) exploration is performed over the parameter set {Ω_b, Ω_cdm, H_0, n_s, A_s, τ, m_WDM, f_iso, n_iso}. Broad, non‑informative priors are placed on f_iso and n_iso, while standard priors are used for the ΛCDM parameters. The sampler (PolyChord within MontePython) generates over a million posterior samples, ensuring convergence.

Results for the pure WDM case (f_iso = 0) reproduce existing limits: the 95 % credible lower bound is m_WDM > 1.8 keV. When a CDM isocurvature component with f_CDM = 0.01 (corresponding to f_iso ≈ 10⁻⁴) is allowed, the bound relaxes dramatically to m_WDM > 0.27 keV. The posterior prefers a blue isocurvature spectral index n_iso ≈ 4.2 ± 0.3, consistent with the Planck upper limit on isocurvature amplitude (A_iso ≲ 0.06 A_ad). The degeneracy between f_iso and n_iso follows an approximate linear relation: larger f_iso can compensate for a smaller n_iso tilt, and vice versa. This “shallow degeneracy” indicates that modest isocurvature power can offset the free‑streaming suppression without violating CMB constraints.

The authors discuss the physical implications. The CDI compensation operates primarily on scales of 100–1000 kpc (k ≈ 10 Mpc⁻¹), an intermediate regime between the large‑scale CMB/BAO constraints and the very small scales probed by Lyman‑α forest or strong lensing. Consequently, while sub‑keV WDM can now evade the UVLF constraints, it does not automatically solve the core‑cusp or too‑big‑to‑fail problems that manifest on even smaller scales. Moreover, an excessively blue isocurvature spectrum could overproduce power at the smallest scales, re‑introducing tension with Lyman‑α data; thus the viable region is a narrow band in the (f_iso, n_iso) plane.

Future observations will sharpen these conclusions. Deeper JWST surveys will extend the UVLF to fainter magnitudes and higher redshifts, tightening the link between halo abundance and small‑scale power. 21 cm intensity mapping and global signal experiments will directly probe the matter power spectrum at comparable scales, offering an independent test of the CDI compensation. If forthcoming data continue to allow f_iso ≈ 10⁻⁴ with n_iso ≈ 4, sub‑keV thermal relics could remain a plausible dark‑matter candidate, providing a natural mechanism for kiloparsec‑scale cores without invoking extreme baryonic feedback.

In summary, this work provides the first comprehensive Bayesian analysis that combines CMB, BAO, supernovae, and high‑z UV luminosity functions to assess the “warm + cold‑isocurvature” scenario. It demonstrates that a modest CDM isocurvature component can relax the thermal WDM mass bound by more than a factor of six, opening a previously excluded region of parameter space for sub‑keV warm dark matter. The study highlights both the promise and the limitations of this mechanism, and outlines clear observational pathways for future verification.