Effect of Accelerated Global Expansion on Bending of Light

Abstract

In 2007 Rindler and Ishak showed that, contrary to previous claims, the value of the cosmological constant does have an effect on light deflection by a gravitating object in an expanding universe, modeled by a Schwarzschild-de~Sitter spacetime. In this paper we consider light bending in the more general situation of a gravitating object in a cosmological background with varying expansion rate $H(t)$. We calculate numerically the null geodesics representing light rays deflected by a black hole in an accelerating Friedmann-Lemaître-Robertson-Walker universe, modeled by a McVittie metric. Keeping the values of the distances from the observer to the lensing object and to the source fixed, we plot the dependence of the bending angle measured by two different sets of observers in this spacetime on the rate of change of $H(t)$.

12 pages, 4 figures

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• Direct Probe of Dark Energy through Gravitational Lensing Effect
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• Beyond lensing by the cosmological constant
• Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light
• Light bending by the cosmological constant
• Cosmological applications of the Brown-York quasilocal mass
• Influence of cosmological expansion in local experiments
• Simultaneous baldness and cosmic baldness and Kottler spacetime
• Gravitational lensing in a universe with matter and a cosmological constant
• Limits on the Inferred Hubble Constant Bias from a Local McVittie Gravitational Field