Estimating weak lensing convergence correlation of Type-Ia supernovae from 5-year SNLS data by internal error estimate technique

TL;DR

This paper detects a non-zero weak lensing convergence correlation among Type-Ia supernovae using 5-year SNLS data, employing internal error estimation and bootstrap techniques to reliably estimate the correlation function and covariance matrix.

Contribution

It introduces an internal error estimate technique combined with bootstrap resampling to accurately measure weak lensing convergence correlations from limited supernova data.

Findings

Detected non-zero weak lensing convergence correlation signal

Demonstrated reliable covariance matrix estimation with bootstrap resampling

Validated the effectiveness of internal error estimation for small datasets

Abstract

We report non-zero weak lensing convergence correlation signal of Type-Ia supernovae from 5-year Supernovae Legacy Survey data. For our analysis we utilize 296 supernovae magnification data from 5-year SNLS in the weak lensing limit. The data we use consists of measurements from four different patches, each covering 1 square degree of the sky, merged together. We demonstrate that it is possible to have a very good estimate of the two point correlation function from this data using internal error estimate technique. In order to have a good estimate of the corresponding covariance matrix we apply bootstrap spatial re-sampling technique where we reshuffle the original data consisting of 296 data points 100-10000 times and compare the results with that obtained from original data points. We show that this technique helps us arrive at a reliable conclusion on weak lensing convergence even though the original dataset comprises of a small number of data points. This also allows us to compute the corresponding covariance matrix with great accuracy.