The Distance-Redshift Relation for Universes with no Intergalactic Medium

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

doi:10.1086/180961

Cited by 178 publications

(202 citation statements)

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“…In addition, there is a log-correction which comes from the logarithmic growth of matter perturbations during the radiation era. We shall take it into account only for the dominant term C (5) ℓ . Furthermore, we use that during the matter dominated era 4πGa…”

Section: Results For a Pure Cdm Universementioning

confidence: 99%

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Fluctuations of the luminosity distance

2006

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We derive an expression for the luminosity distance in a perturbed Friedmann universe. We define the correlation function and the power spectrum of the luminosity distance fluctuations and express them in terms of the initial spectrum of the Bardeen potential. We present semi-analytical results for the case of a pure CDM (cold dark matter) universe. We argue that the luminosity distance power spectrum represents a new observational tool which can be used to determine cosmological parameters. In addition, our results shed some light into the debate whether second order small scale fluctuations can mimic an accelerating universe.PACS numbers: 98.62.En, 98.80.Es, 98.62.Py

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Section: Results For a Pure Cdm Universementioning

confidence: 99%

“…Therefore, it is of great importance to derive a general formula of the luminosity distance in a universe with perturbations. To some extent, this has been done in several papers before [4,5]. But the formula which we derive here is new.…”

Section: Introductionmentioning

confidence: 88%

Fluctuations of the luminosity distance

2006

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“…After Dyer & Roeder [16], it is usual to introduce a phenomenological parameter, α = 1 − ρ cl <ρm> , called the "smoothness" parameter. Such a parameter quantifies the portion of matter in clumps (ρ cl ) relative to the amount of background matter which is uniformly distributed (ρ m ).…”

Section: Zkdr Equation For Luminosity Distancementioning

confidence: 99%

“…When α = 1 (filled beam), the FRW case is fully recovered; α < 1 stands for a defocusing effect; α = 0 represents a totally clumped universe (empty beam). The distance relation that takes the mass inhomogeneities into account is usually named Dyer-Roeder distance [16], although its theoretical necessity had been previously studied by Zeldovich [17] and Kantowski [18]. In this way, we label it here as Zeldovich-Kantowski-Dyer-Roeder (ZKDR) distance formula (for an overview on cosmic distances taking into account the presence of inhomogeneities see the paper by Kantowski[19]).…”

Section: Introductionmentioning

confidence: 99%

Constraining the dark energy and smoothness parameter with supernovae

2008

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The presence of inhomogeneities modifies the cosmic distances through the gravitational lensing effect, and, indirectly, must affect the main cosmological tests. Assuming that the dark energy is a smooth component, the simplest way to account for the influence of clustering is to suppose that the average evolution of the expanding Universe is governed by the total matter-energy density whereas the focusing of light is only affected by a fraction of the total matter density quantified by the α DyerRoeder parameter. By using two different samples of SNe type Ia data, the Ωm and α parameters are constrained by applying the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) luminosity distance redshift relation for a flat (ΛCDM) model. A χ 2 -analysis using the 115 SNe Ia data of Astier et al. sample (2006) constrains the density parameter to be Ωm = 0.26 +0.17 −0.07 (2σ) while the α parameter is weakly limited (all the values ∈ [0, 1] are allowed even at 1σ). However, a similar analysis based the 182 SNe Ia data of Riess et al. (2007) constrains the pair of parameters to be Ωm = 0.33 +0.09 −0.07 and α ≥ 0.42 (2σ). Basically, this occurs because the Riess et al. sample extends to appreciably higher redshifts. As a general result, even considering the existence of inhomogeneities as described by the smoothness α parameter, the Einstein-de Sitter model is ruled out by the two samples with a high degree of statistical confidence (11.5σ and 9.9σ, respectively). The inhomogeneous Hubble-Sandage diagram discussed here highlight the necessity of the dark energy, and a transition deceleration/accelerating phase at z ∼ 0.5 is also required.

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“…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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The Distance-Redshift Relation for Universes with no Intergalactic Medium

Cited by 178 publications

References 0 publications

Fluctuations of the luminosity distance

Fluctuations of the luminosity distance

Constraining the dark energy and smoothness parameter with supernovae

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

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