Determining the neutrino lifetime from cosmology

We explore the cosmological signals of theories in which the neutrinos decay into invisible dark radiation after becoming nonrelativistic. We show that, in this scenario, near-future large-scale structure measurements from the Euclid satellite, when combined with cosmic microwave background data from Planck, may allow an independent determination of both the lifetime of the neutrinos and the sum of their masses. These parameters can be independently determined, because the Euclid data will cover a range of redshifts, allowing the growth of structure over time to be tracked. If neutrinos are stable on cosmological timescales, these observations can improve the lower limit on the neutrino lifetime by 7 orders of magnitude, from $\mathcal{O}(10)$ to $2\times {10}^8\mathrm{yr}$ (95% C.L.), without significantly affecting the measurement of neutrino mass. On the other hand, if neutrinos decay after becoming nonrelativistic but on timescales less than $\mathcal{O}(100)$ million years, these observations may allow not just the first measurement of the sum of neutrino masses, but also the determination of the neutrino lifetime from cosmology.

Figure 1

Evolution of the ratio of the $\mathrm{CDM}+\mathrm{baryon}$ density perturbations with respect to the case of massless neutrinos. The blue (black) curve corresponds to the case of stable (unstable) massive neutrinos with $\sum m_{\nu }=0.25\mathrm{eV}$. Here $z_{\text{decay}}$, defined as the redshift at which the neutrino width ${\mathrm{\Gamma }}_{\nu }$ becomes equal to the Hubble constant, corresponds to the redshift at the time of neutrino decay. Similarly, $z_{\mathrm{nr}}$ denotes the redshift at which 80% of the neutrinos have become nonrelativistic. Unstable heavier neutrinos with $\sum m_{\nu }=0.3\mathrm{eV}$ (red) can give the same density perturbation at low redshift as stable neutrinos of mass $\sum m_{\nu }=0.25\mathrm{eV}$. However, at $z=2$, the perturbation in the heavier neutrino scenario deviates at the $\mathcal{O}(0.1)\%$ level from the stable neutrino scenario (purple arrow).

Figure 2

Forecast of the 2D posterior of the sum of neutrino masses (at 68% C.L.) and decay width of the heaviest neutrino (at 95% C.L.) reconstructed from a combination of $\mathrm{Planck}+\mathrm{Euclid}$ $P(k)+\mathrm{Euclid}$ lensing. The fiducial model assumes that neutrinos are stable and that they follow the normal ordering (left panel) or inverted ordering (right panel).

Figure 3

The same as Fig. 2, but the fiducial model now assumes decaying neutrinos with $({\mathrm{Log}}_{10}[{\mathrm{\Gamma }}_{\nu }/(\mathrm{km}/\mathrm{s}/\mathrm{Mpc})],\sum m_{\nu }/\mathrm{eV})=(3.7,0.16)$ (left panel) and (3,0.25) (right panel) in the normal ordering. The stars and dashed lines indicate the fiducial values of the corresponding parameters.