Effect of the spatial curvature on light bending and time delay in curved Einstein-Straus--de Sitter spacetime

Abstract

A method of general applicability has been developed, whereby the null geodesic equations of the Einstein-Straus-de Sitter metric can be integrated simultaneously in terms of the curvature constant $k$. The purpose is to generalize the computation of light deflection and time delay by a spherical mass distribution. Assuming a flat Universe with most recent measurements of the Hubble constant $H_0$ and the cosmological constant $\Lambda$, five time delays between the four bright images of the lensed quasar SDSS J1004+4112 have been forecasted and compared to others in the field. In addition, we have reviewed the question of the possible contribution of a positive $\Lambda$ to reduce the light bending, and concluded that the changes are seemingly too small to be appreciable on cosmological scales. The same conclusion has been reached regarding the time delay. Having addressed the question of the effect of the spatial curvature in both closed and open Universe, we have found that the strong lensing is slightly affected by the expected small curvature density ${\Omega }_{k0}$ of the current Universe within its error bar $|{\Omega }_{k0}|⪅0.001$, in such a way that it may safely be neglected. However, it's only if ${\Omega }_{k0}$ gets quite larger that the effect being noticeable. While it is only theoretically possible for ${\Omega }_{k0}$ to be higher, it's worthwhile to stress that this should impact the light bending and time delay, causing them to decrease or increase depending upon whether the spatial curvature is positive or negative. Furthermore, one can infer that the observed light deflection and time delay independently, that are found to be significantly deviated from those of the flat Universe, may serve as a useful means to provide constraints on ${\Omega }_{k0}$, thus making the approach employed in this work more promising than others.

arXiv comment22 pages, 6 figures, 8 tables

References in corpus (38)

• The Mass Distribution of SDSS J1004+4112 Revisited
• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• A Gravitationally Lensed Quasar with Quadruple Images Separated by 14.62 Arcseconds
• Observations and Theoretical Implications of the Large Separation Lensed Quasar SDSS J1004+4112
• On the influence of the cosmological constant on gravitational lensing in small systems
• The Rewards of Patience: An 822 Day Time Delay in the Gravitational Lens SDSS J1004+4112
• An Improved Method to Measure the Cosmic Curvature
• Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations
• The role of Lambda in the cosmological lens equation
• Rigorous Approach to the Gravitational Lensing
• Discovery of a Fifth Image of the Large Separation Gravitationally Lensed Quasar SDSS J1004+4112
• A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies
• Bending of light in novel 4$D$ Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method
• On lensing by a cosmological constant
• Does Cosmological Term Influence Gravitational Lensing?
• Cosmological constant and lensing
• Models of the giant quadruple quasar SDSS J1004+4112
• Chandra Observations of SDSS J1004+4112: Constraints on the Lensing Cluster and Anomalous X-Ray Flux Ratios of the Quadruply Imaged Quasar
• Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant
• Strong lensing in the Einstein-Straus solution
• Cosmological effects in the local static frame
• Classical tests of general relativity in the Newtonian limit of Schwarzschild-de Sitter spacetime
• Gravitational Lensing Corrections in Flat LambdaCDM Cosmology
• Cosmological constant and time delay
• The Longest Delay: a 14.5 Yr Campaign to Determine the Third Time Delay in the Lensing Cluster SDSS~J1004+4112
• Constraints on cosmic curvature with lensing time delays and gravitational waves
• Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results
• Lensing in an interior Kottler solution
• Time Delays for the Giant Quadruple Lensed Quasar SDSS J1004+4112: Prospects for Determining the Density Profile of the Lensing Cluster
• Dark energy, curvature, and cosmic coincidence
• Time Delay in Swiss Cheese Gravitational Lensing
• A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints From the Third Time Delay
• Effect of the spatial curvature of the Universe on the form of the gravitational potential
• Time delay in the Einstein-Straus solution
• Deflection of light and time delay in closed Einstein-Straus solution
• The Embedded Transparent Lens and Fermat's Least-Time Principle
• The Gravitational Lens Equation for Embedded Lenses; Magnification and Ellipticity
• Image Properties of Embedded Lenses

Cited by in corpus (2)

• Deflection of light and time delay in hyperbolic Einstein-Straus--de Sitter solution
• Lensing in matched exterior and interior Kottler solutions