Visible in the laboratory and invisible in cosmology: Decaying sterile neutrinos

The expansion history and thermal physical process that happened in the early Universe before big bang nucleosynthesis (BBN) remains relatively unconstrained by observations. Low reheating temperature universes with normalcy temperatures of $T_{\mathrm{RH}}\sim 2\mathrm{MeV}$ remain consistent with primordial nucleosynthesis and accommodate several new physics scenarios that would normally be constrained by high-temperature reheating models, including massive sterile neutrinos. We explore such scenarios’ production of keV-scale sterile neutrinos and their resulting constraints from cosmological observations. The parameter space for massive sterile neutrinos is much less constrained than in high-$T_{\mathrm{RH}}$ thermal histories, though several cosmological constraints remain. Such parameter space is the target of several current and upcoming laboratory experiments such as TRISTAN (KATRIN), HUNTER, MAGNETO-$\nu$, and PTOLEMY. Cosmological constraints remain stringent for stable keV-scale sterile neutrinos. However, we show that sterile neutrinos with a dark decay to radiation through a $Z^{\prime }$ or a new scalar are largely unconstrained by cosmology. In addition, this mechanism of sterile neutrinos with large mixing may provide a solution to the Hubble tension. We find that keV-scale sterile neutrinos are therefore one of the best probes of the untested pre-BBN era in the early Universe and could be seen in upcoming laboratory experiments.

Figure 1

Shown here is the parameter space for a possible low reheating temperature universe with $T_{\mathrm{RH}}=5\mathrm{MeV}$, for the case of ${\nu }_s\leftrightarrow {\nu }_e$ mixing. The regions of this figure are described in the beginning of Sec. 3.

Figure 2

Shown here is the calculated production and energy density evolution for massless standard neutrinos (black line) and an example of $m_s=100\mathrm{keV}$ sterile neutrinos. We show five different ${\sin }^{2}2\theta$ cases of sterile neutrino energy density evolution ${\rho }_{{\nu }_s}$. The sterile neutrinos decay at different times (temperatures) ranging from a case that matches the neutrino’s mass $T_{\text{decay}}=0.1\mathrm{MeV}$ (red line) down to the temperature of matter radiation equality (green line). Note that sterile neutrinos with very different initial production densities can all match the same density relative to the active neutrinos at their decay. Therefore, a wide range of sterile neutrino masses and ${\sin }^{2}2\theta$ can match a designated $N_{\mathrm{eff}}$, when combined with either a nearly fully thermalized or nonthermalized ${\rho }_{{\nu }_{\alpha }}$ in LRT cosmologies. The reheating temperature in this example is chosen to be 5 MeV. The moments of $T=m_s$ and $T_{\mathrm{rm}}$ are shown with the dotted and dashed vertical lines, respectively.

Figure 3

Shown are the updated parameter spaces of dark decay in an LRT universe for two cases, $T_{\mathrm{RH}}=1.8$ and $7\mathrm{MeV}$, left and right, respectively. The diagonal reddish and blueish lines correspond to the cases when the decay happens at the temperature of matter-radiation equality and match different $N_{\mathrm{eff}}$ values. For each pair, the darker color (lower) is associated with a value of $N_{\mathrm{eff},\mathrm{Std}}=3.044$ and the lighter color one $N_{\mathrm{eff},\mathrm{H}0}=3.48$ [34]. For the darker shaded region, $N_{\mathrm{eff}}$ ranges from the minimal provided by $N_{\mathrm{eff},\mathrm{act}}$ to the standard value with a contribution from sterile neutrino decay. In the lighter shaded region on the right panel, $N_{\mathrm{eff}}$ ranges from the standard value to that preferred to alleviate the Hubble tension, $N_{\mathrm{eff},\mathrm{H}0}$. Above the lighter diagonal, the parameter space can accommodate an alleviation of the Hubble tension with $N_{\mathrm{eff},\mathrm{H}0}$ or provide the standard density $N_{\mathrm{eff},\mathrm{Std}}$. For the case of $T_{\mathrm{RH}}=1.8\mathrm{MeV}$, the thermal nature of the CMB [67] constrains the red hatched portion. This constraint does not apply for $T_{\mathrm{RH}}=7\mathrm{MeV}$ in this parameter space.