A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies

TL;DR

This paper establishes new observational upper bounds on the cosmological constant by analyzing the relativistic bending of light around galaxies and clusters, incorporating the $$ contribution into the lens equation.

Contribution

It introduces an amended lens equation accounting for $$ effects and derives the tightest observational limits on $$ from gravitational lensing data.

Findings

The $$ contribution to light bending can be larger than second-order terms.

New upper bounds on $$ are close to cosmological constraints.

The method improves limits on dark energy effects from gravitational lensing.

Abstract

We derive new limits on the value of the cosmological constant, $\Lambda$, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of $\Lambda$ to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild-de Sitter vacuole exactly matched into a Friedmann-Robertson-Walker background and show that a $\Lambda$-contribution term appears in the deflection angle within the lens equation. 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 $\Lambda$. 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.