Gravitational lens equation for embedded lenses; magnification and ellipticity

Chen, Bin; Kantowski, R.; Dai, Xinyu

doi:10.1103/physrevd.84.083004

Cited by 10 publications

(31 citation statements)

References 22 publications

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“…These two parameters are not independent if the source and deflector redshifts are fixed. Because of the nonlinearity of the expressions, we were only able to give an iterative procedure which allowed us to numerically evaluate the conventional minimum impact Schwarzschild coordinate r 0 as a function of 1 [3]. We have since been able to analytically carry out this iterative procedure [see Eq.…”

Section: Introductionmentioning

confidence: 99%

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Image properties of embedded lenses

2012

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We give analytic expressions for image properties of objects seen around point mass lenses embedded in a flat ÃCDM universe. An embedded lens in an otherwise homogeneous universe offers a more realistic representation of the lense's gravity field and its associated deflection properties than does the conventional linear superposition theory. Embedding reduces the range of the gravitational force acting on passing light beams thus altering all quantities such as deflection angles, amplifications, shears and Einstein ring sizes. Embedding also exhibits the explicit effect of the cosmological constant on these same lensing quantities. In this paper, we present these new results and demonstrate how they can be used. The effects of embedding on image properties, although small, i.e., usually less than a fraction of a percent, have a more pronounced effect on image distortions in weak lensing where the effects can be larger than 10%. Embedding also introduces a negative surface mass density for both weak and strong lensing, a quantity altogether absent in conventional Schwarzschild lensing. In strong lensing, we find only one additional quantity, the potential part of the time delay, which differs from conventional lensing by as much as 4%, in agreement with our previous numerical estimates.

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Section: Introductionmentioning

confidence: 99%

“…Derivations of our current results follow the steps given in Refs. [1][2][3] which we will not repeat, but we will instead simply present the new results and use them on two examples.…”

Section: Introductionmentioning

confidence: 99%

Image properties of embedded lenses

2012

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“…(19) and/or (20). To make use of current accretion rate estimates we choose two accreting scenarios: the first, Table I.…”

Section: B Virialized Clustersmentioning

confidence: 99%

“…An that expands with the radius of the background cosmology R(t) but has a constant angular radius θ M as seen by an observer, as the observer ages. In the lowest order lensing theory [19] these radii are related (by embedding) to the Schwarzschild radius r s of the removed mass M d by…”

Section: Introductionmentioning

confidence: 99%

“…We have recently developed the embedded lens theory [17][18][19][20][21][22][23] which could be called the Swiss cheese lens theory, or at lowest order, the compensated lens theory. The theory originated from the Swiss cheese models of general relativity (GR) [24][25][26], therefore one can be confident of its gravitational predictions, if GR is indeed the correct theory.…”

Section: Introductionmentioning

confidence: 99%

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Integrated Sachs-Wolfe effect versus redshift test for the cosmological parameters

2015

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We describe a method using the integrated Sachs-Wolfe (ISW) effect caused by individual inhomogeneities to determine the cosmological parameters, H 0 , Ω m , and Ω Λ , etc. This ISW-redshift test requires detailed knowledge of the internal kinematics of a set of individual density perturbations, e.g., galaxy clusters and/or cosmic voids, in particular their density and velocity profiles, and their mass accretion rates. It assumes the density perturbations are isolated and imbedded (equivalently compensated) and makes use of the newly found relation between the ISW temperature perturbation of the CMB and the Fermat potential of the lens. Given measurements of the amplitudes of the temperature variations in the CMB caused by such clusters or voids at various redshifts and estimates of their angular sizes or masses, one can constrain the cosmological parameters. More realistically, the converse is more likely, i.e., if the background cosmology is sufficiently constrained, measurement of ISW profiles of clusters and voids (e.g., hot and cold spots and rings) can constrain dynamical properties of the dark matter, including accretion, associated with such lenses and thus constrain the evolution of these objects with redshift.PACS numbers: 98.62. Sb, 98.65.Dx,

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Embedded Lensing Time Delays, the Fermat Potential, and the Integrated Sachs–wolfe Effect

Chen¹,

Kantowski²,

Dai³

2015

ApJ

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We derive the Fermat potential for a spherically symmetric lens embedded in an FLRW cosmology and use it to investigate the late-time integrated Sachs-Wolfe (ISW) effect, i.e., secondary temperature fluctuations in the cosmic microwave background (CMB) caused by individual large scale clusters and voids. We present a simple analytical expression for the temperature fluctuation in the CMB across such a lens as a derivative of the lens' Fermat potential. This formalism is applicable to both linear and nonlinear density evolution scenarios, to arbitrarily large density contrasts, and to all open and closed background cosmologies. It is much simpler to use and makes the same predictions as conventional approaches. In this approach the total temperature fluctuation can be split into a time-delay part and an evolutionary part. Both parts must be included for cosmic structures that evolve and both can be equally important. We present very simple ISW models for cosmic voids and galaxy clusters to illustrate the ease of use of our formalism. We use the Fermat potentials of simple cosmic void models to compare predicted ISW effects with those recently extracted from WMAP and Planck data by stacking large cosmic voids using the aperture photometry method. If voids in the local universe with large density contrasts are no longer evolving we find that the time delay contribution alone predicts values consistent with the measurements. However, we find that for voids still evolving linearly, the evolutionary contribution cancels a significant part of the time delay contribution and results in predicted signals that are much smaller than recently observed.

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Gravitational lens equation for embedded lenses; magnification and ellipticity

Cited by 10 publications

References 22 publications

Image properties of embedded lenses

Image properties of embedded lenses

Integrated Sachs-Wolfe effect versus redshift test for the cosmological parameters

Embedded Lensing Time Delays, the Fermat Potential, and the Integrated Sachs–wolfe Effect

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