Abstract
We present the gaugeinvariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source restframe and the observed angle and redshift measured in the observer restframe. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gaugeinvariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the EB decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.
Original language  English 

Article number  A2405 
Journal  Journal of Cosmology and Astroparticle Physics 
Volume  2018 
Issue number  4 
DOIs  
Publication status  Published  9 Apr 2018 
Keywords
 Cosmological perturbation theory
 Gravitational lensing
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Data availability statement for 'Gaugeinvariant formalism of cosmological weak lensing'.
Yoo, J. (Creator), Grimm, N. (Creator), Mitsou, E. (Creator), Amara, A. (Creator) & Refregier, A. (Creator), IOP Publishing, 9 Apr 2018
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