Non-thermal neutrino-like hot dark matter in light of the $S_8$ tension

Abstract

The $\Lambda$CDM prediction of $S_8\equiv {\sigma }_8({\Omega }_m/0.3{)}^{0.5}$ -- where ${\sigma }_8$ is the root mean square of matter fluctuations on a 8 $h^{-1}$Mpc scale -- once calibrated on Planck CMB data is $2-3\sigma$ lower than its direct estimate by a number of weak lensing surveys. In this paper, we explore the possibility that the '$S_8$-tension' is due to a non-thermal hot dark matter (HDM) fractional contribution to the universe energy density leading to a power suppression at small-scales in the matter power spectrum. Any HDM models can be characterized by its effective mass $m_{sp}^{\mathrm{eff}}$ and its contribution to the relativistic degrees of freedom at CMB decoupling $\Delta N_{\mathrm{eff}}$. Taking the specific example of a sterile particle produced from the decay of the inflaton during a matter dominated era, we find that from Planck only the tension can be reduced below $2\sigma$, but Planck does not favor a non-zero $m_{sp}^{\mathrm{eff}},\Delta N_{\mathrm{eff}}$. In combination with a measurement of $S_8$ from KIDS1000+BOSS+2dfLenS, the $S_8$-tension would hint at the existence of a particle of mass $m_{sp}^{\mathrm{eff}}\simeq 0.67_{-0.48}^{+0.26}$ $\mathrm{eV}$ with a contribution to $\Delta N_{\mathrm{eff}}\simeq 0.06\pm 0.05$. However, Pantheon and BOSS BAO/$f{\sigma }_8$ data restricts the particle mass to $m_{sp}^{\mathrm{eff}}\simeq 0.48_{-0.36}^{+0.17}$ and contribution to $\Delta N_{\mathrm{eff}}\simeq 0.046_{-0.031}^{+0.004}$. We discuss implications of our results for other canonical non-thermal HDM models -- the Dodelson-Widrow model and a thermal sterile particle with a different temperature in the hidden sector. We report competitive results on such hidden sector temperature which might have interesting implications for particle physics model building, in particular connecting the $S_8$-tension to the longstanding short baseline oscillation anomaly.

Comments: accepted Physical Review D, new figures, references and discussion added conclusion is same