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 $z\sim 0.5$.

Figure 1

The 3D power spectrum variance of SNe Ia flux fluctuations, which is the sum of ${\Delta }_v^2(\overrightarrow{k})\equiv Q^2(z)k^3{P}_{3\mathrm{D}}^v(\overrightarrow{k})/(2{\pi }^2)$ (solid lines) and ${\Delta }_L^2(\overrightarrow{k})\equiv 4k^3{P}_{3D}^{\kappa }(\overrightarrow{k})/(2{\pi }^2)$ (dotted lines), at $z\in [0.45,0.55]$. $k$ is in units of $h/\mathrm{Mpc}$. Gravitational lensing lacks small scale power along the l.o.s., which causes the oscillating features. For the same reason, there is significant suppression in ${\Delta }_L^2(\overrightarrow{k})$ at $k_{\parallel }\gg 2\pi /\Delta x$, where LSPV can be measured accurately in a model independent way. When $k_{\parallel }\to 0$, ${\Delta }_L^2(\overrightarrow{k})$ is barely suppressed and ${\Delta }_v^2(\overrightarrow{k})$ cannot be measured for these modes. ${\Delta }_L^2$ begins to increase where $k_{\perp }\to 0$, because of its dependence on $C_{l=k_{\perp }{x}_c}^{\kappa }$. Note that ${\Delta }_L^2(\overrightarrow{k})$ is slightly asymmetric with respect to $\theta \to \pi -\theta$. The ensemble average of ${\Delta }_L^2$ can be calculated from independent lensing surveys. After subtraction, gravitational lensing only induces statistical error (long-dashed lines), which is estimated by combining all ${\theta }_{\max }\times {\theta }_{\max }$ patches in half the sky.