A roadmap to cosmological parameter analysis with thirdorder shear statistics. II. Analytic covariance estimate
Abstract
Context. Thirdorder weak lensing statistics are a promising tool for cosmological analyses since they extract cosmological information in the nonGaussianity of the cosmic largescale structure. However, such analyses require precise and accurate models for the covariance of the statistics.
Aims: In this second paper of a series on thirdorder weak lensing statistics, we derive and validate an analytic model for the covariance of the thirdorder aperture statistics «M_{ap}^{3}».
Methods: We derive the covariance model from a realspace estimator for «M_{ap}^{3}», including the Gaussian and nonGaussian parts. We validate the model by comparing it to estimates from simulated Gaussian random fields (GRFs) and two sets of Nbody simulations. Finally, we perform mock cosmological analyses with the model covariance and the simulation estimate to compare the resulting parameter constraints.
Results: We find good agreement between the analytic model and the simulations, both for the GRFs and the Nbody simulations. The figure of merit in the S_{8} − Ω_{m} plane from our covariance model is within 3% of the one obtained from the simulated covariances. We also show that our model, which is based on an estimator using convergence maps, can be used to obtain upper and lower bounds for the covariance of an estimator based on threepoint shear correlation functions. This second estimator is required to measure «M_{ap}^{3}» in realistic survey data. In our derivation, we find that the covariance of «M_{ap}^{3}» cannot be obtained from the bispectrum covariance and that it includes several `finitefield terms' that do not scale with the inverse survey area.
Conclusions: Our covariance model is sufficiently accurate for analysing stage III surveys. Covariances for statistics in Fourier space cannot always be straightforwardly converted into covariance for realspace statistics.
The modelling code is available at https://github.com/sheydenreich/threepoint/releases
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 2023
 DOI:
 10.1051/00046361/202245652
 arXiv:
 arXiv:2212.04485
 Bibcode:
 2023A&A...672A.185L
 Keywords:

 gravitational lensing: weak;
 cosmological parameters;
 methods: statistical;
 largescale structure of Universe;
 methods: analytical;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 21 pages + appendix, 16 figures, 1 table