## 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 et al., which accounts for the characteristic non-Gaussian distribution caused by lensing magnication 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 intrinsicdispersion in magnitudes is independent of redshift, we and

standard deviation level, although we note that in tests on simulations, this model tends to overestimate the magnitude of the intrinsic dispersion, and underestimate

*σ*_{8}= 0:44^{+0:63}_{-0:44}at the onestandard deviation level, although we note that in tests on simulations, this model tends to overestimate the magnitude of the intrinsic dispersion, and underestimate

*σ*_{8}. We note that the degeneracy between intrinsic dispersion and the effects of*σ*_{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 and*σ*_{8}= 1:07^{+0:50}_{-0:76}.Original language | English |
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Pages (from-to) | 259-272 |

Number of pages | 14 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 467 |

Issue number | 1 |

Early online date | 23 Dec 2016 |

DOIs | |

Publication status | Published - 11 May 2017 |

## Keywords

- cosmology
- large scale structure of the universe - cosmology
- observation - cosmology
- theory - galaxies
- kinematics and dynamics - galaxies
- statistics
- RCUK
- STFC
- ST/N000668/1