The impact of weak lensing on Type Ia supernovae luminosity distances

Abstract

When Type Ia supernovae are used to infer cosmological parameters, their luminosities are compared to those from a homogeneous cosmology. In this note we propose a test to examine to what degree SN Ia have been observed on lines of sight where the average matter density is \textit{not} representative of the homogeneous background. We apply our test to the Pantheon SN Ia compilation, and find two redshift bins which indicate a moderate bias to over-density at $\sim 2\sigma$. We modify the Tripp estimator to explicitly de-lens SN Ia magnitudes, and show that this reduces scatter of Hubble diagram residuals. Using our revised Tripp estimator, the effect on cosmological parameters from Pantheon in $\Lambda$CDM is however small with a change in mean value from ${\Omega }_{\mathrm{m}}=0.317\pm 0.027$ (baseline) to ${\Omega }_{\mathrm{m}}=0.312\pm 0.025$ (de-lensed). For the Flat $w$CDM case it is ${\Omega }_{\mathrm{m}}=0.332\pm 0.049$ and $w=-1.16\pm 0.16$ (baseline) versus ${\Omega }_{\mathrm{m}}=0.316\pm 0.048$ and $w=-1.12\pm 0.15$ (de-lensed). We note that the effect of lensing on cosmological parameters may be larger for future high-z surveys.

arXiv comment4 pages, 3 figures. Accepted by MNRAS

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