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, 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 Sigma m(nu) less than or similar to 0.31 eV, sigma(w(0)) less than or similar to 0.02, and sigma(w(a)) less than or similar to 0.18 (1-sigma CL) in the Sigma m(nu)-w(0)-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 similar to 33%. We also allow Omega(CDM) to vary as well as Sigma m(nu), w(0) and w(a), and demonstrate how these constraints degrade as a consequence.