The impact of weak lensing on Type Ia supernovae luminosity distances

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 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 ∼2σ. 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 ΛCDM is however small with a change in mean value from Ωm = 0.317 ± 0.027 (baseline) to Ωm = 0.312 ± 0.025 (de-lensed). For the Flat wCDM case it is Ωm = 0.332 ± 0.049 and w = −1.16 ± 0.16 (baseline) versus Ωm = 0.316 ± 0.048 and w = −1.12 ± 0.15 (de-lensed). We note that the effect of lensing on cosmological parameters may be larger for future high-z surveys.