Accurate weak lensing of standard candles. I. Flexible cosmological fits

TL;DR

This paper introduces a fast, accurate statistical approximation for weak lensing effects on standard candles like supernovae, enabling improved cosmological parameter estimation and potential constraints from lensing data.

Contribution

It provides simple, accurate fits for lensing magnification moments and variance, facilitating efficient likelihood analyses and enabling the use of lensing to constrain cosmology.

Findings

Statistical approximation matches N-body simulations with high accuracy.

Shifted lognormal distribution effectively models lensing magnification.

Fits enable faster, reliable cosmological parameter estimation.

Abstract

With the availability of thousands of type Ia supernovae in the near future the magnitude scatter induced by lensing will become a major issue as it affects parameter estimation. Current N-body simulations are too time consuming to be integrated in the likelihood analyses used for estimating the cosmological parameters. In this paper we show that in the weak lensing regime a statistical numerical approximation produces accurate results orders of magnitude faster. We write down simple fits to the second, third and fourth central moments of the lensing magnification probability distribution as a function of redshift, of the power spectrum normalization and of the present-day matter density. We also improve upon existing models of lensing variance and show that a shifted lognormal distribution fits well the numerical one. These fits can be easily employed in cosmological likelihood analyses. Moreover, our theoretical predictions make it possible to invert the problem and begin using supernovae lensing to constrain the cosmological parameters.