Forecasting Constraints on Non-Thermal Light Massive Relics from Future CMB Experiments (CMB-S4/Simons Observatory)

TL;DR

This study assesses how future CMB experiments constrain non-thermal Light Massive Relics (LiMRs) produced by inflaton/moduli decay or in the Dodelson-Widrow scenario. Using Fisher forecasts, the authors quantify constraints on two phenomenological parameters, $ΔN_ ext{eff}$ and $M_ ext{sp}^ ext{eff}$, and show that heavier LiMRs yield tighter $ΔN_ ext{eff}$ constraints while near-recombination transition timing governs the strength of the lensing signal and parameter correlations. They demonstrate that, when the first two moments are matched, LiMRs with different production histories yield similar cosmological constraints, and CMB-S4 is not sensitive to higher moments of the distribution. A higher-precision, CV-limited survey could begin to distinguish certain higher-moment differences, but in general linear CMB data alone cannot disentangle different non-thermal distributions beyond the first two moments. The work highlights the importance of combining CMB with LSS and non-linear probes to fully characterize LiMRs and their early-Universe production mechanisms.

Abstract

In this work we present Fisher forecasts on \textit{non-thermal 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 non-thermally distributed dark sector particles, and also comparing our results with those for sterile particles following the Dodelson-Widrow distribution. Two independent parameters, $ΔN_\mathrm{eff}$ and $M_\mathrm{sp}^\mathrm{eff}$, influence linear cosmological observables. We find $ΔN_\mathrm{eff}$ to be more tightly constrained (by a factor of $10$) for a less abundant, heavier LiMR which becomes fully non-relativistic around matter-radiation equality than a more abundant, lighter LiMR which becomes fully non-relativistic just after recombination. The uncertainties on $M_\mathrm{sp}^\mathrm{eff}$ differ by a factor of $\sim3$ between the two cases. Our analysis also reveals distinct parameter correlations: the phenomenological parameters $\{ΔN_\mathrm{eff},M_\mathrm{sp}^\mathrm{eff}\}$ 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.

Figures (17)

• Figure 1: Plots of various auto-correlation signal and noise spectra for the inflaton/moduli decay model with the parameter values from Table \ref{['tab:tab_fid']} (set I).
• Figure 2: Comparative plot of the inflaton decay (NT) and Dodelson-Widrow (DW) distributions for $\{\Delta N_\rm{eff},M_\rm{sp}^\rm{eff}\}=\{0.034,0.903~\rm{eV}\}$. The momenta and the distribution function are both in units of $T_\rm{ncdm,0}$ which is calculated using Eq. (\ref{['Tncdm0']}) with $m_\phi=10^{-6}M_\rm{Pl},\tau=10^8/m_\phi,$ and $B_\rm{sp}=0.0118$ for the NT model.
• Figure 3: Comparison of the residuals of the TT, EE, and $\phi\phi$ spectra for the two sets of fiducial values. The progressively darker shaded regions correspond respectively to the $1\sigma$ error bars associated with the particular configurations of the SO-LAT experiment, the CMB-S4 experiment, and to the CV-limited experiment considered in this work (see Table \ref{['tab2']}).
• Figure 4: The posterior distributions and Fisher ellipses for the parameters $\{\omega_m=\omega_b+\omega_\rm{cdm},h,\Delta N_\rm{eff},M_\rm{sp}^\rm{eff}\}$ (plotted using getdist) for the CMB-S4 experiment.
• Figure 5: Comparative Fisher plots for CMB-S4.