The effects of velocities and lensing on moments of the Hubble diagram

Understand

We consider the dispersion on the supernova distance-redshift relation due to peculiar velocities and gravitational lensing, and the sensitivity of these effects to the amplitude of the matter power spectrum.

• We use the MeMo lensing likelihood developed by Quartin, Marra & Amendola (2014), which accounts for the characteristic non-Gaussian distribution caused by lensing magnification with measurements of the first four central moments of the distribution of magnitudes.
• We build on the MeMo likelihood by including the effects of peculiar velocities directly into the model for the moments.
• In order to measure the moments from sparse numbers of supernovae, we take a new approach using Kernel Density Estimation to estimate the underlying probability density function of the magnitude residuals.