A new independent limit on the cosmological constantdark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

Ishak, Mustapha; Rindler, Wolfgang; Dossett, Jason; Moldenhauer, Jacob; Allison, C.

doi:10.1111/j.1365-2966.2008.13468.x

Cited by 57 publications

(155 citation statements)

References 53 publications

(82 reference statements)

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“…We note at this point that within the Schwarzschildde Sitter metric, the magnitude of the effects of the cosmological constant Λ > 0 on the bending of light from distant galaxies is still an open issue. At present, there are several approaches to the subject, giving different answers, in which the order of magnitude of the effects ranges from zero [7] or unobservably small [8] to appreciable one [9,10]. Our considerations in this paper pertain to local effects of the cosmological constant, which are discussed within the Special Relativity framework.…”

Section: Linearized Gravity In the Presence Of A Cosmological Conmentioning

confidence: 99%

Cosmological constant and local gravity

2010

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We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and Λ > 0, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations (due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive.

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Section: Linearized Gravity In the Presence Of A Cosmological Conmentioning

confidence: 99%

Cosmological constant and local gravity

2010

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“…Note that this is analogous to the vacuole model of a structure inside the Einstein radius discussed in e.g. [10,22] and references therein, for ΛCDM.…”

Section: Introductionmentioning

confidence: 59%

“…To the best of our knowledge, the first of the successful computations regarding the effect of the dark energy in the light bending phenomenon appeared in [8,9,10]. It was shown in [9] that even though Λ does not appear explicitly in the bending equation, in the expression for the bending angle it appears indeed, via an inner product to define the angle and the first order Λ-contribution was shown to be −ΛR 3 0 /6M G, where R 0 is the distance of the closest approach.…”

Section: Introductionmentioning

confidence: 99%

“…(We shall elucidate this so called Rindler-Ishak method, technically in Section 4. Further in [10], the existing lensing data for large scale structures was used in this formalism and a new, independent upper bound of the cosmological constant, Λ 10 −50 m −2 , was found. Since this initiation, considerable efforts are being paid to pursue various aspects of this novel phenomenon, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Light bending, static dark energy, and related uniqueness of Schwarzschild–de Sitter spacetime

Ali

Bhattacharya

2018

Phys. Rev. D

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Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to −1, apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turn around radius, RTA,max, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state P (r) = αρ(r) as a source in Ref.[1], which reproduced the expression for RTA,max found earlier in the cosmological McVittie spacetime. Here we show that the equality originates from the equivalence of geodesic motion in these two backgrounds, in the nonrelativistic regime. We extend this metric up to the third order and compute the bending of light using the Rindler-Ishak method. For α = −1, a dark energy dependent term appears in the bending equation, unlike the case of the cosmological constant, α = −1. Due to this new term in particular, existing data for the light bending at galactic scales yields, (1 + α) O(10 −14 ), thereby practically ruling out any such static and inhomogeneous dark energy fluid we started with. Implication of this result pertaining the uniqueness of the Schwarzschild-de Sitter spacetime in such inhomogeneous dark energy background is discussed.

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“…In addition, it would not be correct to argue that a Λ as small as ≈10 −56 cm −2 (as inferred from the cosmological observations) cannot contribute to the physics appreciably in the local problems. It has been shown recently that even this value of Λ does indeed contribute to the bending of light and to the advance of the perihelion of planets [31].…”

Section: Different Pieces Fit Togethermentioning

confidence: 99%

Einstein and Beyond: A Critical Perspective on General Relativity

Vishwakarma

2016

Universe

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An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T ik and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to T ik . Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation R ik = 0 as the field equation of gravitation plus inertia in the very presence of matter.

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A new independent limit on the cosmological constantdark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

Cited by 57 publications

References 53 publications

Cosmological constant and local gravity

Cosmological constant and local gravity

Light bending, static dark energy, and related uniqueness of Schwarzschild–de Sitter spacetime

Einstein and Beyond: A Critical Perspective on General Relativity

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