Type Ia supernovae as speed sensors at intermediate redshifts

The application of large scale peculiar velocity (LSPV), as a crucial probe of dark matter, dark energy and gravity, is severely limited by measurement obstacles. We show that fluctuations in type Ia supernovae (SNe Ia) 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. Advance in SN observations can further significantly reduce shot noise induced by SN intrinsic fluctuations, which is the dominant statistical error. Robust mapping on the motion of the dark universe through SNe Ia is thus feasible to $z\sim 0.5$.