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

Edward Robert Mark Macaulay, T. M. Davis, Dario Scovacricchi, David Bacon, Thomas Collett, Bob Nichol

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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 σ8 = 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 σ8. We note that the degeneracy between intrinsic dispersion and the effects of σ8 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 σ8 = 1:07+0:50-0:76.
Original languageEnglish
Pages (from-to)259-272
Number of pages14
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
Early online date23 Dec 2016
Publication statusPublished - 11 May 2017


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


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