The general theory of secondary weak gravitational lensing
- Astrophysics, Cosmology and Gravity Centre, and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, 7701 South Africa (South Africa)
Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes in the gravitational field across the scale of the ray bundle of light propagating to us, resulting in the familiar arcs in lensed images. This is normally called the flexion, and is approximated by Taylor expanding the shear and magnification across the image plane. However, the physical origin of this effect arises from higher-order corrections in the geodesic deviation equation governing the gravitational force between neighbouring geodesics— so involves derivatives of the Riemann tensor. We show that integrating the second-order geodesic deviation equation results in a 'Hessian map' for gravitational lensing, which is a higher-order addition to the Jacobi map. We derive the general form of the Hessian map in an arbitrary spacetime paying particular attention to the separate effects of local Ricci versus non-local Weyl curvature. We then specialise to the case of a perturbed FLRW model, and give the general form of the Hessian for the first time. This has a host of new contributions which could in principle be used as tests for modified gravity.
- OSTI ID:
- 22525385
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 09; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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