Constraining neutrino mass and dark energy with peculiar velocities and lensing dispersions of Type Ia supernovae

We show that peculiar velocities of Type Ia supernovae can be used to derive constraints on the sum of neutrino masses, $\mathrm{\Sigma }{m}_{\nu }$, and dark energy equation of state, $w=w_0+w_a(1-a)$, from measurements of the magnitude-redshift relation, complementary to galaxy redshift and weak lensing surveys. Light from a supernova propagates through a perturbed Universe so the luminosity distance is modified from its homogeneous prediction. This modification is proportional to the matter density fluctuation and its time derivative due to gravitational lensing and peculiar velocity respectively. At low redshifts, the peculiar velocity signal dominates while at high redshifts lensing does. We show that using lensing and peculiar velocity of supernovae from the upcoming surveys WFIRST and ZTF, without other observations, we can constrain $\mathrm{\Sigma }{m}_{\nu }\lesssim 0.31\mathrm{eV}$, $\sigma (w_0)\lesssim 0.02$, and $\sigma (w_a)\lesssim 0.18$ $(1–\sigma \mathrm{CL})$ in the $\mathrm{\Sigma }{m}_{\nu }\text{−}{w}_0\text{−}{w}_a$ parameter space, where all the other cosmological parameters are fixed. We find that adding peculiar velocity information from low redshifts shrinks the volume of the parameter ellipsoid in this space by $\sim 33\%$. We also allow ${\mathrm{\Omega }}_{\mathrm{CDM}}$ to vary as well as $\mathrm{\Sigma }{m}_{\nu },w_0$ and $w_a$, and demonstrate how these constraints degrade as a consequence.

Figure 1

Lensing- (blue solid) and velocity- (red dashed) induced scatter, ${\sigma }^2$, in magnitude as a function of the sum of neutrino masses, $m_{\nu }$, in eV for a source at $z=0.02$ (top) and $z=1$ (bottom). The velocity scatter has been rescaled to have the same amplitude as lensing scatter at $\mathrm{\Sigma }{m}_{\nu }=0.06\mathrm{eV}$ to enable better comparison of slopes. Lensing scatter has a larger slope, and so is more sensitive to the sum of neutrino masses.

Figure 2

Dependence of magnitude scatter, ${\sigma }^2$, sourced by lensing (blue solid), peculiar velocities (red dashed), and intrinsic (green dotted) on source redshift ($z$), for $\mathrm{\Sigma }{m}_{\nu }=0.06\mathrm{eV}$. Lensing produces a large scatter at higher source redshifts while velocities produce a large scatter at lower source redshifts. The intrinsic scatter is independent of source redshift.

Figure 3

Expected supernova distribution for ZTF [26] (top) and WFIRST [25] (bottom).

Figure 4

Expected constraints on $w_0$ and sum of neutrino masses $m_{\nu }$ in eV from the full supernova samples of ZTF and WFIRST (top left), ZTF alone (bottom left) and WFIRST alone (bottom right). Red dashed curves show the 1- and $2\text{−}\sigma$ constraints when using lensing scatter alone. Blue filled regions denote the same when using both lensing and peculiar velocities. Note that all other cosmological parameters have been fixed to their fiducial values for these constraints. At low redshifts (bottom left) peculiar velocities are crucial to derive any meaningful constraints on the sum of neutrino masses from supernovae alone.

Figure 5

Joint constraints on $\mathrm{\Sigma }{m}_{\nu }$, $w_0$, and $w_a$ with all other cosmological parameters fixed, using the full supernova samples of ZTF and WFIRST. As before, red dashed lines show constraints when using lensing alone, while blue filled regions show constraints when adding peculiar velocities. Note also that varying $w_a$ weakens the neutrino mass constraint, as evident from the larger range of $m_{\nu }$ (eV) compared to Fig. 4. There is no improvement in $w_0$ but $w_a$ and $m_{\nu }$ are still better constrained when peculiar velocities are added.

Figure 6

Joint constraints on ${\mathrm{\Omega }}_{\mathrm{CDM}},\mathrm{\Sigma }{m}_{\nu },w_0$, and $w_a$ with all other cosmological parameters fixed. As before, red dashed lines show constraints when using lensing alone, while blue filled regions show constraints when adding peculiar velocities. Varying ${\mathrm{\Omega }}_{\mathrm{CDM}}$ simultaneously degrades constraints by a factor of $\sim 2$, and once again we scale the $m_{\nu }$ axis to account for the weaker constraint.