Partially Thermalized eV-Scale Sterile Neutrinos in Dynamical Dark Energy and Non-Flat Cosmologies

Abstract

We investigate cosmological constraints on a $(3+1)$ neutrino framework containing an additional partially thermalized, eV-scale sterile neutrino alongside the three active species. Rather than assuming full thermalization, we allow the sterile abundance to vary independently through its physical mass $m_s$ and contribution $ΔN_{\rm eff}$ to the effective number of relativistic species. The sterile state is modeled as a thermally distributed non-cold relic with a temperature below that of the active-neutrino background. We consider flat and non-flat $Λ$CDM and $w_0w_a$CDM cosmologies, all including the same $(3+1)ν$ sector. The models are constrained using Planck 2018 CMB data, DESI DR2 BAO, Pantheon+ Type Ia supernovae, a conservative compilation of $fσ_8$ measurements, and the recent H0DN. Oscillation-informed priors are imposed on the active-neutrino mass splittings, while the eV scale sterile-mass range is motivated by short-baseline oscillation searches and global $(3+1)$ analyses. We find that allowing additional freedom in the late-time cosmological background substantially changes the inferred sterile-neutrino sector. The effective sterile mass increases from $m_{s,\rm eff}\sim0.11\pm0.05~{\rm eV}$ in flat $Λ$CDM$+(3+1)ν$ to $\sim0.35\pm0.12~{\rm eV}$ in the non-flat $w_0w_a$CDM$+(3+1)ν$ model. The corresponding sterile abundance shifts from $ΔN_{\rm eff}\lesssim0.1$ to $ΔN_{\rm eff}\simeq0.35\pm0.15$, while remaining well below the fully thermalized limit, $ΔN_{\rm eff}\simeq1$. The non-flat $w_0w_a$CDM models also show $\sim 2.8σ$ preference for open spatial geometry, $Ω_k\simeq0.0045\pm0.0016$, and yield $H_0\simeq70.9\pm0.7~{\rm km\,s^{-1}\,Mpc^{-1}}$ and $S_8\simeq0.785\pm0.015$. These models improve the minimum $χ^2$ by approximately $21$-$25$ relative to flat $Λ$CDM$+(3+1)ν$.