Hunting Thermal Relics in the DESI DR1 Ly$α$ Forest
We investigate constraints on additional relativistic species and thermal sterile neutrinos using the DESI DR1 one-dimensional Lyman-$α$ forest power spectrum, combined with Planck 2018 CMB and DESI DR2 BAO measurements. We consider both the $Λ$CDM+$N_{\rm eff}$ extension and a thermal with a different-temperature sterile-neutrino (DTS) scenario, in which the sterile relic can be colder than the standard neutrino background. We first validate the DESI two-parameter $P_{\rm 1D}$ compression for the DTS model, finding that the residual cosmological dependence not captured by the compressed parameters remains below 0.15%. No significant evidence for additional radiation or a sterile component is found. For $Λ$CDM+$N_{\rm eff}$, we obtain $N_{\rm eff}<3.41$ at 95% credibility from CMB+DESI-BAO+DESI-$P_{\rm 1D}$. In the DTS scenario, the full CMB+DESI-BAO+DESI-$P_{\rm 1D}$ combination yields the stringent bound $m_s^{\rm eff}<0.061\,{\rm eV}$, highlighting the complementarity of BAO and Lyman-$α$ information in constraining the massive sterile abundance. We further interpret the allowed $ΔN_{\rm eff}$ in terms of thermal light relics, deriving lower limits on their decoupling temperatures that reach the QCD epoch.