Scale Invariance in a Perturbed Einstein-De Sitter Cosmology

Abdalla, Élcio; Mohayaee, Roya; Ribeiro, Marcelo B.

doi:10.1142/s0218348x0100083x

“…(16) In other words, Hubble-law deviations occur in higher redshift ranges than deviations from OH. This was first noticed in Ribeiro (1995), discussed again in R01b and explored further in Abdalla et al (2001) by means of a simple perturbed model. As discussed at length in R01b, OH corresponds to a constant value of observational average density, that is, when this average density is calculated along the chosen spacetime's past null cone.…”

Section: Observational Inhomogeneity Of the Einstein-de Sitter Spacetimementioning

confidence: 73%

“…This alternative conceptual framework grew out of various works (Ribeiro 1992a(Ribeiro ,b, 1993(Ribeiro , 1994(Ribeiro , 1995(Ribeiro , 2001aAbdalla et al 2001) and was comprehensively analyzed in Ribeiro (2001b;hereafter R01b). Albani et al (2007; hereafter A07) further developed this alternative perspective in a somewhat condensed version.…”

Section: Introductionmentioning

confidence: 99%

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Lemos

¹

,

Ribeiro

²

2008

A&A

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Context. An important aim of standard relativistic cosmology is the empirical verification of its geometrical concept of homogeneity by considering various definitions of distance and astronomical observations occurring along the past light cone. Aims. We analyze the physical consequences of distinguishing between spatial homogeneity (SH), defined by the Cosmological Principle, and observational homogeneity (OH). We argue that OH is falsifiable by means of astronomical observations, whereas SH can be verified only indirectly. Methods. We simulate observational counts of cosmological sources, such as galaxies, by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes are derived using the various cosmological-distance definitions in the EdS cosmological model. The observational volumes and simulated counts are then used to derive differential densities. We present the behavior of these densities for increasing redshift values. Results. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. In addition, simulated counts with no OH features at low redshift begin to show OH characteristics at high redshift. The comoving distance appears to be the only distance definition for which both SH and OH are applicable simultaneously, even though with limitations. Conclusions. We demonstrate that observations indicative of a possible absence of OH do not necessarily falsify the standard Friedmannian cosmology, which implies that this cosmology does not always produce observable homogeneous densities. We conclude that using different cosmological distances in the characterization of the galaxy distribution can produce significant ambiguities in reaching conclusions about the large-scale galaxy distribution in the Universe.

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“…In other words, Hubble-law deviations occur in higher redshift ranges than deviations from OH. This was first noticed in Ribeiro (1995), discussed again in R01b and explored further in Abdalla et al (2001) by means of a simple perturbed model. As discussed at length in R01b, OH corresponds to a constant value of observational average density, that is, when this average density is calculated along the chosen spacetime's past null cone.…”

Section: Observational Inhomogeneity Of the Einstein-de Sitter Spacetimementioning

confidence: 73%

“…This alternative conceptual framework grew out of various works (Ribeiro 1992ab, 1993(Ribeiro 1992ab, , 1994(Ribeiro 1992ab, , 1995(Ribeiro 1992ab, , 2001aAbdalla et al 2001) and was comprehensively analyzed in Ribeiro (2001b;hereafter R01b). Albani et al (2007; hereafter A07) further developed this alternative perspective in a somewhat condensed version.…”

Section: Introductionmentioning

confidence: 99%

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Lemos,

Ribeiro

2008

Preprint

Self Cite

0

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Context. An important aim of standard relativistic cosmology is the empirical verification of its geometrical concept of homogeneity by considering various definitions of distance and astronomical observations occurring along the past light cone. Aims. We analyze the physical consequences of distinguishing between spatial homogeneity (SH), defined by the Cosmological Principle, and observational homogeneity (OH). We argue that OH is falsifiable by means of astronomical observations, whereas SH can be verified only indirectly. Methods. We simulate observational counts of cosmological sources, such as galaxies, by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes are derived using the various cosmological-distance definitions in the EdS cosmological model. The observational volumes and simulated counts are then used to derive differential densities. We present the behavior of these densities for increasing redshift values. Results. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. In addition, simulated counts with no OH features at low redshift begin to show OH characteristics at high redshift. The comoving distance appears to be the only distance definition for which both SH and OH are applicable simultaneously, even though with limitations. Conclusions. We demonstrate that observations indicative of a possible absence of OH do not necessarily falsify the standard Friedmannian cosmology, which implies that this cosmology does not always produce observable homogeneous densities. We conclude that using different cosmological distances in the characterization of the galaxy distribution can produce significant ambiguities in reaching conclusions about the large-scale galaxy distribution in the Universe.

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“…Inhomogeneous cosmological models have been searched by many authors [2] [7]. The fact that detailed maps show quite strong inhomogeneities has been a motivation for long controversies [8] [9].…”

mentioning

confidence: 99%

A numerical study on the dimension of an extremely inhomogeneous matter distribution

Chirenti¹

2005

Braz. J. Phys.

0

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We have developed an algorithm that numericaly computes the dimension of an extremely inhomogeneous matter distribution, given by a discrete hierarchical metric. With our results it is possible to analise how the dimension of the matter density tends to d = 3 , as we consider larger samples.Most authors believe that the large scale distribution of matter should be a constant, as predicted by Einstein's cosmological principle, but there is also a belief that such an idea should be further checked against observation [1]. Some authors argued quite convincingly that the large scale distribution of matter should be fractal, quite the oposite to that expected by the cosmological principle. In a previous work [10], we have presented a study on a toy model given by the hierarchical metricwhere the metric is defined on all integers, depending on their decomposition in terms of powers of 2 aswhere k, , m and n are integers. We obtained the following expression for the matter density,by means of the Einstein equations. Computing the Christoffel symbols and subsequently the curvature tensor for this metric requires some care, since we are not dealing with derivatives of functions, but differences of functions defined on a discrete space.We speculated whether such a matter distribution could be described by a fractal. As it turned out, from our preliminary analisis (see [10]), the dimension of the matter density tends slowly to d = 3.Considering the relationwhere K is some constant, and the constant d is the fractal dimension of the matter density [11], it is easy to see that it impliesfor large r. We have numerically computed N(r) and the plot ln N(r) × ln r, in figure (1), showing that equation (5), although valid at very large r), is a good approximation for the behavior of the data.

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Scale Invariance in a Perturbed Einstein-De Sitter Cosmology

Cited by 18 publications

References 23 publications

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

A numerical study on the dimension of an extremely inhomogeneous matter distribution

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