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

TL;DR

This paper investigates how peculiar velocities and gravitational lensing influence supernova distance measurements, developing a new method to estimate these effects and applying it to real data to constrain cosmological parameters.

Contribution

It introduces an enhanced likelihood model incorporating peculiar velocities into supernova magnitude moments, utilizing Kernel Density Estimation for sparse data, and applies this to the JLA catalogue.

Findings

Estimated σ8 around 0.44 with large uncertainties when intrinsic dispersion is free.

Fixed intrinsic dispersion yields σ8 approximately 1.07 with broad confidence intervals.

Degeneracy between intrinsic dispersion and matter fluctuation amplitude affects parameter constraints.

Abstract

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. We also describe a bootstrap re-sampling approach to estimate the data covariance matrix. We then apply the method to the Joint Light-curve Analysis (JLA) supernova catalogue. When we impose only that the intrinsic dispersion in magnitudes is independent of redshift, we find $\sigma_8=0.44^{+0.63}_{-0.44}$ at the one standard deviation level, although we note that in tests on simulations, this model tends to overestimate the magnitude of the intrinsic dispersion, and underestimate $\sigma_8$. We note that the degeneracy between intrinsic dispersion and the effects of $\sigma_8$ is more pronounced when lensing and velocity effects are considered simultaneously, due to a cancellation of redshift dependence when both effects are included. Keeping the model of the intrinsic dispersion fixed as a Gaussian distribution of width 0.14 mag, we find $\sigma_8 = 1.07^{+0.50}_{-0.76}$.