Jacobi Mapping Approach for a Precise Cosmological Weak Lensing Formalism

TL;DR

This paper introduces the Jacobi mapping formalism as a gauge-invariant, accurate method for describing relativistic effects in cosmological weak lensing, addressing limitations of the standard approach for future high-precision surveys.

Contribution

It demonstrates that the Jacobi mapping approach provides gauge-invariant expressions for weak lensing observables, including scalar, vector, and tensor perturbations, improving accuracy over the standard formalism.

Findings

Rotation vanishes to linear order in this formalism

Additional tensor mode term in cosmic shear components

Supports gauge-invariant weak lensing formalism for precision cosmology

Abstract

Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism yields gauge-dependent results and, hence, does not meet the level of accuracy demanded by the next generation of weak lensing surveys. Here, we show that the Jacobi mapping formalism provides a solid alternative to the standard formalism, as it accurately describes all the relativistic effects contributing to the weak lensing observables. We calculate gauge-invariant expressions for the distortion in the luminosity distance, the cosmic shear components and the lensing rotation to linear order including scalar, vector and tensor perturbations. In particular, the Jacobi mapping formalism proves that the rotation is fully vanishing to linear order. Furthermore, the cosmic shear components contain an additional term in tensor modes which is absent in the results obtained with the standard formalism. Our work provides further support and confirmation of the gauge-invariant lensing formalism needed in the era of precision cosmology.