The Contribution of The Cosmological Constant/Dark Energy to The Bending of Light Revisited: Applications To Gravitational Lensing, Time Delays and an Upper-bound on The Cosmological Constant

Details The Contribution of The Cosmological Constant/Dark Energy to The Bending of Light Revisited: Applications To Gravitational Lensing, Time Delays and an Upper-bound on The Cosmological Constant The Contribution of The Cosmological Constant/Dark Energy to The Bending of Light Revisited: Applications To Gravitational Lensing, Time Delays and an Upper-bound on The Cosmological Constant

May 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aas...212.5207i&link_type=abstract

American Astronomical Society, AAS Meeting #212, #52.07; Bulletin of the American Astronomical Society, Vol. 40, p.249

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We report new results on the effect of the cosmological constant Lambda on the bending of light by a spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, Lambda does indeed contribute to the bending of light. We use this result to derive an amended lens equation in which the contribution of Lambda to the Einstein deflection angle is taken into account. We apply the result to observations of Einstein radii around several systems where the lens is a distant galaxy or a cluster of galaxies. We find that the contribution of the Lambda-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of the cosmological constant. These limits constitute the best observational upper bound on Lambda after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints. Next, we show that the result expands to the time delay expressions. While it is known that Lambda contributes to the gravitational time delay, it is shown here that a new Lambda-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out. We show that our results derive from various methods including the exact matching of solutions to Einstein's equations, approximations used in gravitational lensing, and Fermat's Principle.

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