Sterile neutrinos: Cosmology versus short-baseline experiments

Cosmology and short-baseline (SBL) neutrino oscillation data both hint at the existence of light sterile neutrinos with masses in the 1 eV range. Here we perform a detailed analysis of the sterile neutrino scenario using both cosmological and SBL data. We have additionally considered the possibility that the extra neutrino degrees of freedom are not fully thermalized in the early universe. Even when analyzing only cosmological data we find a preference for the existence of massive sterile neutrinos in both ($3+1$) and ($3+2$) scenarios, and with the inclusion of SBL data the evidence is formally at the $3.3\sigma$ level in the case of a ($3+1$) model. Interestingly, cosmological and SBL data both point to the same mass scale of approximately 1 eV. In the ($3+1$) framework $\mathrm{WMAP}9+\mathrm{SPT}$ provide a value of the sterile mass eigenstate $m_4=(1.72\pm 0.65)\mathrm{eV}$; this result is strengthened by adding the prior from SBL posterior to $m_4=(1.27\pm 0.12)\mathrm{eV}$ [$m_4=(1.23\pm 0.13)\mathrm{eV}$ when data from the Sloan Digital Sky Survey is also considered in the cosmological analysis]. In the ($3+2$) scheme, two additional, nonfully thermalized neutrinos are compatible with the whole set of cosmological and SBL data, leading to mass values of $m_4=(0.95\pm 0.30)\mathrm{eV}$ and $m_5=(1.59\pm 0.49)\mathrm{eV}$. The inclusion of Planck data does not change our considerations about the mass scale; concerning the extra neutrino degrees of freedom, by invoking a partial thermalization the $3+1$ model is still consistent with the latest data.

Figure 1

Allowed $3\sigma$ regions (99.73% C.L.) in the ${sin}^{2}2{\vartheta }_{e\mu }-\Delta m_{41}^2$ plane in the $3+1$ model obtained from ${\nu }_e$ and ${\overline{\nu }}_e$ disappearance data (left of the dark red curve), ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ disappearance data (left of the dark green curve), combined disappearance data (left of the dark orange curve), ${\nu }_{\mu }\to {\nu }_e$ and ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ appearance data (inside the blue curve), and from the global fit (inside the red curves). The best-fit points in the last two cases are indicated by crosses.

Figure 2

Case (B): $N_{\mathrm{eff}}^{\prime }$ massive neutrinos with total mass $\sum _{}^{}{m}_{\nu }$. Two-dimensional marginalized 68% and 95% confidence level regions in the plane $\sum _{}^{}{m}_{\nu }$ versus $N_{\mathrm{eff}}^{\prime }$. Leftmost (red) contours refer to CMB-only data ($\mathrm{WMAP}9+\mathrm{SPT}+\mathrm{ACT}$), while rightmost (blue) contours also include BAO and HST. The larger (green) area denotes the results for $\mathrm{WMAP}9+\mathrm{SPT}$ data sets.

Figure 3

Case (B): $N_{\mathrm{eff}}^{\prime }$ massive neutrinos with total mass $\sum _{}^{}{m}_{\nu }$. One-dimensional marginalized posteriors for $N_{\mathrm{eff}}^{\prime }$ (left panel) and $\sum _{}^{}{m}_{\nu }$ (right panel). Solid (red) lines refer to CMB-only data ($\mathrm{WMAP}9+\mathrm{SPT}+\mathrm{ACT}$), while dashed (blue) lines also include BAO and HST. The dot-dashed (green) curve denotes the results for $\mathrm{WMAP}9+\mathrm{SPT}$ data sets.

Figure 4

($3+1$) analysis. One-dimensional marginalized posterior for $m_4$. The thick (green) and thin (blue) lines refer to the case of Table  with and without the SBL prior, respectively. Solid lines stand for the analysis on CMB-only ($\mathrm{WMAP}9+\mathrm{SPT}$) data; dot-dashed lines refer to the inclusion of information from the matter power spectrum. The (red) dashed line shows the $3+1$ SBL posterior. 95% C.L. upper bounds on the mass for the different cases are reported as vertical lines.

Figure 5

($3+1$) analysis. Two-dimensional marginalized 68% and 95% confidence-level regions in the plane $N_4-m_4$ for the different combinations of data sets reported in Table .

Figure 6

($3+2$) analysis. One-dimensional marginalized posterior probabilities for $m_4$ (left panel) and $m_5$ (right panel). The thick (green) and thin (blue) lines refer to the case of Table  with and without SBL prior, respectively. Solid lines stand for the analysis on CMB-only ($\mathrm{WMAP}9+\mathrm{SPT}$) data; dot-dashed lines refer to the inclusion of information coming from the matter power spectrum. The (red) dashed line shows the bidimensional $3+2$ SBL posterior marginalized over $m_4$ or $m_5$. 95% C.L. upper bounds on the masses are reported as vertical lines.

Figure 7

($3+2$) analysis. Two-dimensional marginalized 68% and 95% confidence-level regions in the plane ($m_4-m_5$) for the different combinations of data sets reported in Table . The two-dimensional marginalized 95% SBL posterior probability of the $3+2$ model is also overplotted (red solid line).

Figure 8

Reduced ($3+2$) analysis. One-dimensional marginalized posterior probabilities for ($m_4+m_5$). The thick (green) and thin (blue) lines refer to the case of Table  with and without SBL prior, respectively. Solid lines stand for the analysis of CMB-only ($\mathrm{WMAP}9+\mathrm{SPT}$) data; dot-dashed refer to the inclusion of information from the matter power spectrum. The (red) dashed line shows the one-dimensional $3+2$ SBL posterior on ($m_4+m_5$). 95% C.L. upper bounds are also reported (vertical lines).

Figure 9

Reduced ($3+2$) analysis. Two-dimensional marginalized 68% and 95% confidence-level regions in the plane ($N_4+N_5$) versus ($m_4+m_5$) for the different combinations of data sets reported in Table .

Figure 10

($3+1$) analysis. One-dimensional marginalized posterior for $m_4$. The thick (green) and thin (blue) lines refer to the case of Table  with and without the SBL prior, respectively. The (red) dashed line shows the $3+1$ SBL posterior. 95% C.L. upper bounds on the mass for the different cases are reported as vertical lines.

Figure 11

($3+1$) analysis. Two-dimensional marginalized 68% and 95% confidence-level regions in the plane $N_4-m_4$.