Effect of the spatial curvature of the Universe on the form of the gravitational potential

Eingorn, Maxim; Yükselci, A. Emrah; Zhuk, Alexander

doi:10.1140/epjc/s10052-019-7169-6

Cited by 11 publications

(3 citation statements)

References 35 publications

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“…The dependence of the gravitational potential on the spatial curvature in the weak field limit have been proved in Ref. [48], using the same cosmological parameters as ours with realistic small curvature densities [6]. Finally In Ref.…”

Section: Discussionmentioning

confidence: 64%

Deflection of light and time delay in closed Einstein-Straus solution

Guenouche

Zouzou

2018

Phys. Rev. D

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We investigate strong lensing by a spherically symmetric mass distribution in the framework of the Einstein-Straus solution with positive cosmological constant and concentrate on the case of a spatially closed Universe (k = +1). We develop a method based on integration of differential equations in order to make possible the computation of light deflection and time delay. By applying our results to the lensed quasar SDSS J1004+4112, we find that the bending of light and time delay depend on wether the present value of the scale factor a 0 is or is not much smaller than a value close to 9.1 · 10 26 m. Beyond this value, the results are almost the same as for the spatially flat Universe. Moreover, it turns out that a positive cosmological constant attenuates the light bending in agreament with Rindler and Ishak's finding.

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Section: Discussionmentioning

confidence: 64%

Deflection of light and time delay in closed Einstein-Straus solution

Guenouche

Zouzou

2018

Phys. Rev. D

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“…, where we have used (23). Then, employing the conditions δ F J ∼ δ f J , |∂ f J /∂ε J | ∼ 1 and taking into account that time derivatives with respect to η are proportional in order to the Hubble parameter ∼ H , it can be deduced that all three terms in the second line behave as H 2 J ∇(Bδ F J ).…”

Section: Appendix A1: Pressureless Mattermentioning

confidence: 99%

“…Matter sources in [17] have the form of discrete point-like masses, and it is also important to emphasize that no assumptions are made regarding the smallness of the associated energy density contrast, ensuring the validity of the model both at sub-and super-horizon scales. This approach has been further developed in the papers [18][19][20][21][22][23][24][25][26][27]. Particularly in [18,19], generalizations to the case of perfect fluids with the linear p = ωε and nonlinear p = f (ε) equations of state have been performed, i.e.…”

Section: Introductionmentioning

confidence: 99%

Scalar and vector perturbations in a universe with nonlinear perfect fluid

et al. 2021

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We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.

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Duel of cosmological screening lengths

Canay

Eingorn

2020

Physics of the Dark Universe

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Two distinct perturbative approaches have been recently formulated within General Relativity, arguing for the screening of gravity in the ΛCDM Universe. In this paper we compare them and show that the offered screening concepts, each characterized by its own interaction range, can peacefully coexist. Accordingly, we advance a united scheme, determining the gravitational potential at all scales, including regions of nonlinear density contrasts, by means of a simple Helmholtz equation with the effective cosmological screening length. In addition, we claim that cosmic structures may not grow at distances above this Yukawa range and confront its current value with dimensions of the largest known objects in the Universe.As the science rapidly progresses, higher and higher accuracy of observations is achieved. For instance, such a future space mission as Euclid [3,4,5] is designed to probe the Universe expansion with unprecedented precision and impose new restrictions on dark energy, dark matter, and various cosmological parameters. In this connection, the legitimate demand for an advanced theory soars up too. In particular, it is quite natural to expect that Newtonian gravity is modified at large distances and ultimately reconciled with the standard relativistic perturbation theory. By dint of our narration, we aim at sparking interest in two distinct approaches [6,7] relying on General Relativity, which argue that gravity is actually screened, ceasing to be longrange far enough from its every single source. Hereinafter this Yukawa-type screening is sometimes called "cosmological" or "cosmic", since it originates from the presence of the cosmological background.Both cosmic screening approaches have been formulated in the framework of the standard ΛCDM (Λ cold dark matter) model, which is consistent with the observational data [8], though it is noteworthy that currently there is tension between the direct local measurement of the Hubble constant and the value of this very constant following from the Planck data on cosmic microwave background temperature and polarization (see, e.g., [9,10,11]). Furthermore, both original papers [6,7] focus on the matter-and Λ-dominated stages of the Universe evolution, so radiation and relativistic neutrinos are disregarded (though the results of [6] have been subsequently generalized to the case of additional perfect fluids with linear and nonlinear equations of state [12,13,14], as well as to the cases of nonzero spatial curvature [15], f (R) gravity [16] and the phantom braneworld model [17]).From the mathematical point of view, the cosmological Yukawa screening inevitably comes into play when the Einstein equation for the gravitational potential (scalar perturbation) is reduced to the Helmholtz equation, which replaces its popular rival of Poisson type. Meanwhile, the underlying physical reasons and resulting screening ranges are different in [6] and [7]. The scheme of [6] (see additionally [18,19]) is rooted in the so-called discrete cosmology studying how discrete gravitating mass...

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Effect of the spatial curvature of the Universe on the form of the gravitational potential

Cited by 11 publications

References 35 publications

Deflection of light and time delay in closed Einstein-Straus solution

Deflection of light and time delay in closed Einstein-Straus solution

Scalar and vector perturbations in a universe with nonlinear perfect fluid

Duel of cosmological screening lengths

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