Distance-Redshift Relations for Universes with Some Intergalactic Medium

Dyer, C. C.; Roeder, R. C.

doi:10.1086/181146

Cited by 200 publications

(221 citation statements)

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“…Therefore, many authors [2][3][4][5] discussed this issue, but they did not give a simple formula for this relation. Until 1973, Dyer and Roeder [6] The D-R equation is an angular diameter distance-redshift approximate equation that contains a parameter α (named smoothness parameter) for locally inhomogeneous universe, where α (0 ≤ α ≤ 1) describes the influence of local inhomogeneity on the angular diameter distance. The detailed information of the D-R equation and α are displayed in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Yang¹,

Yu²,

Zhang

2013

J. Cosmol. Astropart. Phys.

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Abstract. Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter α to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the DistanceDuality (DD) relation, D L (z)(1 + z) −2 /D A (z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D L and D A are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we use Union2.1 SNe Ia data to constrain the smoothness parameter α and test whether the Dyer-Roeder equation satisfies the DD relation. By using χ 2 minimization, we get α = 0.92 +0.08 −0.32 at 1σ and 0.92 +0.08 −0.65 at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.

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Section: Introductionmentioning

confidence: 99%

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Yang¹,

Yu²,

Zhang

2013

J. Cosmol. Astropart. Phys.

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“…A fruitful approach to clumped matter perturbations of FRW cosmologies, introduced by Dyer & Roeder (1973), is to assume that of all the matter present, a proportion α is uniformly distributed and pressure-free, while the remaining proportion 1 − α is gravitationally bound into clumps. In order to compute the lensing of light beams that remain far from all clumps it suffices to take into consideration the effect of only the uniformly distributed matter.…”

Section: The Averaging Proceduresmentioning

confidence: 99%

“…Schneider et al 1992;Bertotti 1966;Dyer & Roeder 1972,1973, 1974Kantowski 1998). One such technique has been the use of stochastic numerical integration of the lensing equations (Holz & Wald 1998;Dyer & Oattes 1988).…”

Section: Introductionmentioning

confidence: 99%

Cumulative gravitational lensing in Newtonian perturbations of Friedman—Robertson—Walker cosmologies

Claudel

2000

Proc. R. Soc. Lond. A

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Abstract. It is a common assumption amongst astronomers that, in the determination of the distances of remote sources from their apparent brightness, the cumulative gravitational lensing due to the matter in all the galaxies is the same, on average, as if the matter were uniformly distributed throughout the cosmos. The validity of this assumption is considered here by way of general Newtonian perturbations of Friedman-Robertson-Walker (FRW) cosmologies. The analysis is carried out in synchronous gauge, with particular attention to an additional gauge condition that must be imposed. The mean correction to the apparent magnitude-redshift relation is obtained for an arbitrary mean density perturbation. In the case of a zero mean density perturbation, when the intergalactic matter has a dust equation of state, then there is indeed a zero mean first order correction to the apparent magnitude-redshift relation for all redshifts. Point particle and Swiss cheese models are considered as particular cases.

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“…Such distances, D A (˜jz), are solutions to the Dyer-Roeder equation ( Dyer & Roeder 1973;Kantowski 1998), with the matter inhomogeneity parameterized by a local smoothness parameter˜ ( Wang 1999). Because of their simplicity and convenience, Dyer-Roeder distances with fixed values of˜are used to illustrate the effect of weak lensing of point sources, although they do not correctly describe weak lensing (Hamana et al 2000).…”

Section: Introductionmentioning

confidence: 99%

“…For a given redshift z, if a mass fraction˜of the matter in the universe is smoothly distributed, the largest possible distance for light bundles that have not passed through a caustic is given by the Dyer-Roeder distance, the solution to the Dyer-Roeder equation ( Dyer & Roeder 1973;Kantowski 1998):…”

Section: Introductionmentioning

confidence: 99%

Reduced Convergence and the Local Smoothness Parameter: Bridging Two Different Descriptions of Weak‐lensing Amplification

Wang¹,

TenBarge²,

Fleshman³

2005

ApJ

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Weak gravitational lensing due to the inhomogeneous matter distribution in the universe is an important systematic uncertainty in the use of standard candles in cosmology. There are two different descriptions of weak-lensing amplification: one uses a local smoothness parameter˜, and the other uses reduced convergence ¼ 1 þ /j min j (where is convergence). The˜description involves Dyer-Roeder distance D A (˜jz) (˜¼ 1 corresponds to a smooth universe); it is simple and convenient and has been used by the community to illustrate the effect of weak lensing on point sources such as Type Ia supernovae. Wang has previously shown that the˜description can be made realistic by allowing˜to be a local variable, the local smoothness parameter. The description has been used by Wang et al. to derive a universal probability distribution for weak-lensing amplification. In this paper, we bridge the two different descriptions of weak-lensing amplification by relating the reduced convergence and the local smoothness parameter . We give the variance of˜in terms of the matter power spectrum, thus providing a quantitative guidance to the use of Dyer-Roeder distances in illustrating the effect of weak lensing. The by-products of this work include a corrected definition of the reduced convergence and simple and accurate analytical expressions for D A (˜jz). Our results should be very useful in studying the weak lensing of standard candles.

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Distance-Redshift Relations for Universes with Some Intergalactic Medium

Cited by 200 publications

References 0 publications

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Cumulative gravitational lensing in Newtonian perturbations of Friedman—Robertson—Walker cosmologies

Reduced Convergence and the Local Smoothness Parameter: Bridging Two Different Descriptions of Weak‐lensing Amplification

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