Precise measurements of the cosmological impact of dark sector relics can shed light on physics beyond the Standard Model. In this work we present Fisher forecasts on nonthermal light massive relics (LiMR) models for a CMB Stage IV-like experiment and the Simons Observatory—particularly focusing on a model of inflaton/moduli decay giving rise to nonthermally distributed dark sector particles, and also comparing our results with those for sterile particles following the Dodelson-Widrow distribution. Two independent parameters, the effective number of extrarelativistic species $\mathrm{\Delta }{N}_{\mathrm{eff}}$ and the effective mass $M_{\mathrm{sp}}^{\mathrm{eff}}$ of the relic, influence linear cosmological observables. We find $\mathrm{\Delta }{N}_{\mathrm{eff}}$ to be more tightly constrained with $\sigma (\mathrm{\Delta }{N}_{\mathrm{eff}})\sim {10}^{-3}$, for a less abundant, heavier LiMR, which becomes fully nonrelativistic around matter-radiation equality than a more abundant, lighter LiMR, which becomes fully nonrelativistic just after recombination, for which $\sigma (\mathrm{\Delta }{N}_{\mathrm{eff}})\sim {10}^{-2}$. The uncertainties on $M_{\mathrm{sp}}^{\mathrm{eff}}$ differ by a factor of $\sim 3$ between the two cases. Our analysis also reveals distinct parameter correlations: the phenomenological parameters $\{\mathrm{\Delta }{N}_{\mathrm{eff}},M_{\mathrm{sp}}^{\mathrm{eff}}\}$ are found to be negatively correlated for the former case and positively correlated for the latter. We obtain similar projected uncertainties on the cosmological parameters (in either case) for both the inflaton/moduli decay and the Dodelson-Widrow models when the first two moments of the LiMR distribution function, related to the phenomenological parameters, are matched. Finally, by constructing a modified distribution that matches the first two moments of the Dodelson-Widrow but deviates maximally in the third moment, we demonstrate that CMB Stage IV data is not expected to be sensitive to higher moments of the distribution.

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• Cosmic microwave background
• Cosmological parameters
• Dark matter