Optical properties of the Einstein–de Sitter–Kasner universe

Landry, Sylvie; Dyer, C. C.

doi:10.1103/physrevd.56.3307

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…It can be shown that the junction conditions between these two regions are satisfied if we identify our hatted and un-hatted coordinates at the boundary, and if k = 0, b 1 = a −1/2 and b 2 = a [44,46]. The dust dominated regions are then spatially flat FLRW, the vacuum regions are Kasner, and the entire geometry is an exact solution of Einstein's equations [45]. These solutions are, in fact, a special case of the general dust solution admitting a three dimensional group of space-like Killing vectors on two dimensional planar subspaces [23,63], but are chosen such that we can have collapsing regions that do not exhibit the shell crossing singularities that tend to rapidly form in the general case.…”

Section: B Kasner-eds Modelmentioning

confidence: 99%

“…The conditions for these measures to show acceleration, and their relation to observable quantities (if any), is discussed. Section III sets out three different inhomogeneous models: the spherical collapse model, constructed from disjoint FLRW regions; the Kasner-EdS model, an exact solution with alternating expanding vacuum and collapsing dust regions along a line of sight [43][44][45][46][47]; and the Lemaître-Tolman-Bondi model, an exact, spherically-symmetric dust solution [48][49][50]. The volume of space in all of these models is locally decelerating everywhere, and yet we find that observations made within them can still exhibit acceleration.…”

Section: Introductionmentioning

confidence: 99%

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Local and nonlocal measures of acceleration in cosmology

Bull

Clifton

2012

Phys. Rev. D

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Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion. This is often taken to mean that the expansion of space itself is accelerating. In a general spacetime, however, this is not necessarily true. We attempt to clarify this point by considering a handful of local and non-local measures of acceleration in a variety of inhomogeneous cosmological models. Each of the chosen measures corresponds to a theoretical or observational procedure that has previously been used to study acceleration in cosmology, and all measures reduce to the same quantity in the limit of exact spatial homogeneity and isotropy. In statistically homogeneous and isotropic spacetimes, we find that the acceleration inferred from observations of the distance-redshift relation is closely related to the acceleration of the spatially averaged universe, but does not necessarily bear any resemblance to the average of the local acceleration of spacetime itself. For inhomogeneous spacetimes that do not display statistical homogeneity and isotropy, however, we find little correlation between acceleration inferred from observations and the acceleration of the averaged spacetime. This shows that observations made in an inhomogeneous universe can imply acceleration without the existence of dark energy.

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Section: B Kasner-eds Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local and nonlocal measures of acceleration in cosmology

Bull

Clifton

2012

Phys. Rev. D

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show abstract

“…In fact, there has been much recent work (see for example Refs. [21][22][23][24][25]) addressing related questions in the context of "swiss cheese" type cosmologies, where the effects of inhomogeneities on light propagation in the universe have been analyzed. It would be interesting to analyze the case in which all the inhomogeneous regions are described by massive collapsing dust clouds surrounded by an underdense region.…”

Section: Discussionmentioning

confidence: 99%

Gravitational redshift of photons traversing a collapsing dust cloud and observable consequences

Ortiz

Sarbach

2014

Phys. Rev. D

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We analyze the frequency shift of photons propagating on an asymptotically flat spacetime describing a collapsing, spherical dust cloud. We focus on the case where the interaction of the photons with the matter can be neglected. Under fairly general assumptions on the initial data characterizing the collapse, we show that photons with zero angular momentum which travel from past to future null infinity, crossing the collapsing cloud through its center, are always redshifted with respect to stationary observers. We compute this redshift as a function of proper time of a distant stationary observer and discuss its dependency on the mass distribution of the cloud. Possible implications of this redshift effect for weak cosmic censorship and light propagation in cosmological spacetimes are also briefly discussed.

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“…We now wish to consider situations in which we have slices of Einstein-de Sitter geometry sandwiched between regions of Kasner vacuum, repeated over and over again forever. This is a special case of the geometry in Equation (21), which can be shown to explicitly satisfy the required junction conditions between neighbouring regions of dust and vacuum, and hence constitute a viable family of cosmological solution to Einstein's equations [15][16][17]. Although they are too symmetric to describe any realistic astrophysical structures, they do provide an interesting framework to explore ideas about inhomogeneity and anisotropy in the context of exact solutions.…”

Section: Plane Symmetrymentioning

confidence: 99%

Cosmological backreaction in spherical and plane symmetric dust-filled space-times

Clifton

Sussman

2019

Class. Quantum Grav.

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We examine the implementation of Buchert's and Green & Wald's averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert's averaging scheme gives a faithful way of interpreting the large-scale expansion of space, and explicit terms that precisely quantify deviations from the behaviour expected from the Friedmann equations of homogeneous and isotropic cosmological models. The Green & Wald formalism, on the other hand, does not appear to yield any information about the large-scale properties of a given inhomogeneous space-time. Instead, this formalism is designed to calculate the back-reaction effects of shortwavelength fluctuations around a given "background" geometry. We find that the inferred expansion of space in this approach is entirely dependent on the choice of this background, which is not uniquely specified for any given inhomogeneous space-time, and that the "back-reaction" from small-scale structures vanishes in every case we study. This would appear to limit the applicability of Green & Wald's formalism to the study of large-scale expansion in the real Universe, which also has no pre-defined background. Further study is required to enhance the evaluation and comparison of these averaging formalisms, and determine whether the same difficulties exist, in less idealized space-time geometries.

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Optical properties of the Einstein–de Sitter–Kasner universe

Cited by 4 publications

References 17 publications

Local and nonlocal measures of acceleration in cosmology

Local and nonlocal measures of acceleration in cosmology

Gravitational redshift of photons traversing a collapsing dust cloud and observable consequences

Cosmological backreaction in spherical and plane symmetric dust-filled space-times

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