Constraining massive neutrinos using cosmological 21 cm observations

Observations of neutrino oscillations show that neutrinos have mass. However, the best constraints on this mass currently come from cosmology, via measurements of the cosmic microwave background and large-scale structure. In this paper, we explore the prospects for using low-frequency radio observations of the redshifted 21 cm signal from the epoch of reionization to further constrain neutrino masses. We use the Fisher matrix formalism to compare future galaxy surveys and 21 cm experiments. We show that by pushing to smaller scales and probing a considerably larger volume, 21 cm experiments can provide stronger constraints on neutrino masses than even very large galaxy surveys. Finally, we consider the possibility of going beyond measurements of the total neutrino mass to constraining the mass hierarchies. For a futuristic, 21 cm experiment we show that individual neutrino masses could be measured separately from the total neutrino mass.

Figure 1

Effect of a different neutrino mass on the power spectrum at redshifts $z=0.3$ (solid curve), 4 (dashed curve), and 8 (dotted curve). The curves represent the derivatives of the matter power spectrum with respect to neutrino mass for a fiducial mass value of $M_{\nu }=0.3\mathrm{eV}$. The vertical dashed lines represent the nonlinear scale at redshifts $z=0.3$, 4, and 8 (from left to right). Note that the derivative becomes more negative at lower redshifts, as massive neutrinos have more time to affect the power spectrum.

Figure 2

Difference between the power spectra between the normal and inverted hierarchy at different redshifts. We plot the ratio of the power spectrum calculated with total neutrino mass $M_{\nu }=0.12$ distributed in the normal hierarchy (NH, dashed curves) and inverted hierarchy (IH, solid curves) relative to the case where the three neutrino masses are degenerate ($m_1=m_2=m_3$). These curves are calculated at $z=0$ (thin curves) and $z=8$ (thick curves). The difference continues to smaller scales, but saturates at $\sim 0.2\%$ at $k=1h{\mathrm{Mpc}}^{-1}$.

Figure 3

Comparison of angle averaged effective volume for galaxy and 21 cm surveys. SDSS (thin solid curve), G1 (thin dotted curve), G2 (thin short dashed curve), G3 (thin long dashed curve), MWA (thick solid curve), SKA (thick dotted curve), and FFTT (thick dashed curve).

Figure 4

The $2\sigma$ constraints on $M_{\nu }$ (solid curve) from $\mathrm{SKA}+\mathrm{\text{PLANCK}}$ (dotted curve) and $\mathrm{FFTT}+\mathrm{\text{PLANCK}}$ (dashed curve) for the normal (thin curves) and inverted (thick curves) hierarchies.

Figure 5

The 68– % confidence ellipses in the $M_{\nu }\mathrm{\text{−}}w$ plane from PLANCK in combination with SDSS (thin dotted curve), G2 (thin short dashed curve), G1 (thin solid curve), G3 (thin long dashed curve), MWA (thick dotted curve), SKA (thick dashed curve), and FFTT (thick solid curve).

Figure 6

Top panel: $1-\sigma$ fractional errors on the power spectrum at $z=1$ for G3. Bottom panel: $1-\sigma$ fractional errors on the power spectrum at $z=8$ for SKA (thin black points), and FFTT (thick black points). In each panel, we plot the ratio of $P(k)$ for three degenerate masses (dotted curve) or inverted hierarchy (solid curve) to $P(k)$ for the normal hierarchy neutrinos (as in Fig. 2) and $M_{\nu }=0.3\mathrm{eV}$. Only the FFTT has the sensitivity to detect the mass splittings at a significant level. Nonlinearities are expected to affect the $z=1$ power spectrum on scales smaller than $k\gtrsim 0.2h{\mathrm{Mpc}}^{-1}$ and the $z=8$ power spectrum on scales $k\gtrsim 3h{\mathrm{Mpc}}^{-1}$.

Figure 7

The 68% confidence contours on individual neutrino mass states $m_1$, $m_2$, and $m_3$. We show contours for CosmicVar in combination with G3 (long dashed curve), SKA (short dashed curve), and FFTT (solid curve). Fiducial neutrino masses are indicated for the normal hierarchy (diagonal crosses); also shown are the values for the inverted hierarchy (vertical crosses) for $M_{\nu }=0.3\mathrm{eV}$. $\mathrm{\text{CosmicVar}}+\mathrm{FFTT}$ is able to make a weak detection of individual neutrino masses. Insert in the bottom right-hand corner shows the error ellipse in the $m_1+m_2\mathrm{\text{−}}{m}_3$ parameter space and illustrates the strong degeneracy hampers placing tight constraints on individual masses.