Low-scale seesaw models versus $N_{\mathbf{\text{eff}}}$

We consider the contribution of the extra sterile states in generic low-scale seesaw models to extra radiation, parametrized by $N_{\text{eff}}$. We find that the value of $N_{\text{eff}}$ is roughly independent of the seesaw scale within a wide range. We explore the full parameter space in the case of two extra sterile states and find that these models are strongly constrained by cosmological data for any value of the seesaw scale below $\mathcal{O}(100\mathrm{MeV})$.

Figure 1

$\text{Min}[f_{s_i}(T_{\text{max}})]$ for the $i$th sterile state as a function of $M_i$ for a light neutrino spectrum with a NH (thick line) or IH (thin line). The dashed line at 1 corresponds to the minimum value for thermalization.

Figure 2

Sterile neutrino decoupling temperature, $T_d$, as function of the sterile mass for the NH (solid thick line), IH (solid thin line) and for oscillation parameters that minimize $f_s(T_{\text{max}})$ (dashed lines), those that minimize $T_d$ (dotted) and those that minimize $T_d$ while being compatible with bounds from direct searches (solid). The single dashed line satisfies $T=M_i$.

Figure 3

Evolution of the ratio of the number density of sterile species over that of one active massless neutrino for $y=5$ for $(M_1,M_2)\simeq (2\times {10}^{-5},{10}^{-3})$ (solid) and (0.1, 10) (dashed) in MeV and mixing parameters that minimize $f_{s_1}(T_{\text{max}})$ for NH (thick) and IH (thin).

Figure 4

$\mathrm{\Delta }{N}_{\text{eff}}={\epsilon }_s/{\epsilon }_{\nu }^0$ (left) and $\mathrm{\Delta }{N}_{\text{eff}}^{\text{rel}}=({\epsilon }_s-{\epsilon }_s^m)/{\epsilon }_{\nu }^0$ (right) at $T_{\mathrm{W}}$ as a function of the sterile masses NH (upper octant) or IH (lower octant). The thick lines correspond to maximum allowed by BBN at 2$\sigma$.

Figure 5

Distribution of $(|U_{\mu s_i}{|}^2+|U_{\tau s_i}{|}^2)M_i$ versus $|U_{e{s}_i}{|}^2{M}_i$ varying all the unconstrained parameters for NH. The solid/dashed line corresponds to $m_3\sim \sqrt{\mathrm{\Delta }{m}_{\text{atm}}^2}/m_2\sim \sqrt{\mathrm{\Delta }{m}_{\text{solar}}^2}$.