Type Ia supernovae as speed sensors at intermediate redshifts

Large scale peculiar velocity (LSPV) is a crucial probe of dark matter, dark energy, and gravity at cosmological scales. However, its application is severely limited by measurement obstacles. We show that fluctuations in type Ia supernovae fluxes induced by LSPV offer a promising approach to measure LSPV at intermediate redshifts. In the 3D Fourier space, gravitational lensing, the dominant systematical error, is well suppressed, localized, and can be further corrected effectively. Advances in supernova observations can further significantly reduce shot noise induced by supernova intrinsic fluctuations, which is the dominant statistical error. Robust mapping on the motion of the dark universe through type Ia supernovae is thus feasible to z∼0.5.