Reduced Convergence and the Local Smoothness Parameter: Bridging Two Different Descriptions of Weak‐lensing Amplification

Abstract

Weak gravitational lensing due to the inhomogeneous matter distribution in the universe is an important systematic uncertainty in the use of standard candles in cosmology. There are two different descriptions of weak-lensing amplification: one uses a local smoothness parameter˜, and the other uses reduced convergence ¼ 1 þ /j min j (where is convergence). The˜description involves Dyer-Roeder distance D A (˜jz) (˜¼ 1 corresponds to a smooth universe); it is simple and convenient and has been used by the community to illustrate the effect of weak lensing on point sources such as Type Ia supernovae. Wang has previously shown that the˜description can be made realistic by allowing˜to be a local variable, the local smoothness parameter. The description has been used by Wang et al. to derive a universal probability distribution for weak-lensing amplification. In this paper, we bridge the two different descriptions of weak-lensing amplification by relating the reduced convergence and the local smoothness parameter . We give the variance of˜in terms of the matter power spectrum, thus providing a quantitative guidance to the use of Dyer-Roeder distances in illustrating the effect of weak lensing. The by-products of this work include a corrected definition of the reduced convergence and simple and accurate analytical expressions for D A (˜jz). Our results should be very useful in studying the weak lensing of standard candles.

Reconstructing the weak lensing magnification distribution of type Ia supernovae

“…[15,17,24,25,[33][34][35] and references therein. In this UPDF based framework, we first calculate the minimum convergence as [36] κmin (z) = − 3 2…”

Observational signatures of the weak lensing magnification of supernovae

“…The p(µ)'s can be computed numerically using cosmological volume N-body simulations (see for example, [2,16,24,25]). We can derive the p(µ) for an arbitrary cosmological model by using the universal probability distribution function (UPDF) of weak lensing amplification [27,30], with the corrected definition of the minimum convergence [33],…”