A class of shear-free perfect fluids in general relativity. II

Collins, C. B.; White, A. J.

doi:10.1063/1.526316

Cited by 17 publications

(18 citation statements)

References 28 publications

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“…Although being unambiguous, we have to come back to this point later, since a majority of papers on averaging scalar metric inhomogeneities employs Euclidean volume averaging on the background metric in a frame of global coordinates, which do † † Note that a priori the tilt of the 4−velocity relative to the hypersurface normal is not specified. For vanishing tilt, as considered here, and in the case of dust matter, shear-free motion implies homogeneity; this also holds true for large classes of perfect fluid models, see [46,47,45]. We briefly show for the case of dust matter that we can determine the lapse function such that the model is hypersurfacehomogeneous: we use the momentum constraints, K i j||i − K k k|j = 0, for the extrinsic curvature of Eq.…”

Section: Scalar Metric Inhomogeneities In a Metric Form Correspondingmentioning

confidence: 87%

Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects

Buchert¹

2011

Class. Quantum Grav.

142

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We outline the key-steps toward the construction of a physical, fully relativistic cosmology. The influence of inhomogeneities on the effective evolution history of the Universe is encoded in backreaction terms and expressed through spatially averaged geometrical invariants. These are absent and potential candidates for the missing dark sources in the standard model. Since they can be interpreted as energies of an emerging scalar field (the morphon), we are in the position to propose a strategy of how phenomenological scalar field models for Dark Energy, Dark Matter and Inflation, that are usually added as fundamental sources to a homogeneous-geometry (FLRW) cosmology, can be potentially traced back to inhomogeneous geometrical properties of space and its embedding into spacetime. We lay down a line of arguments that is -thus far only qualitatively -conclusive, and we address open problems of quantitative nature, related to the interpretation of observations.We discuss within a covariant framework (i) the foliation problem and invariant definitions of backreaction effects; (ii) the background problem and the notion of an effective cosmology; (iii) generalizations of the cosmological principle and generalizations of the cosmological equations; (iv) dark energies as energies of an effective scalar field; (v) the global gravitational instability of the standard model and basins of attraction for effective states; (vi) multiscale cosmological models and volume acceleration; (vii) effective metrics and strategies for effective distance measurements on the light cone, including observational predictions; (viii) examples of non-perturbative models including explicit backreaction models for the LTB solution, extrapolations of the relativistic Lagrangian perturbation theory, and scalar metric inhomogeneities. The role of scalar metric perturbations is critically examined and embedded into the non-perturbative framework.PACS numbers: 98.80.Cq, 95.35.+d, 95.36.+x, 98.80.Es, 98.80.Jk,

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Section: Scalar Metric Inhomogeneities In a Metric Form Correspondingmentioning

confidence: 87%

Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects

Buchert¹

2011

Class. Quantum Grav.

142

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“…that the Lorentz factor γ is close to 1. Our remark implies that by replacing the approximate sign by an equality sign the fluid has to be shear-free in the metric form {(1) and (2)} and, hence, homogeneous in cosmologically relevant cases [12,13,14].…”

Section: Contextmentioning

confidence: 99%

Cosmological backreaction and its dependence on spacetime foliation

Buchert

Mourier

Roy

2018

Class. Quantum Grav.

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The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einstein's equations that is coordinate-independent and only functionally depends on a metric. This formalism is applicable to general 3 + 1 foliations of spacetime for an arbitrary fluid with tilted flow. We clarify the dependence on spacetime foliation and argue that this dependence is weak in cosmological settings. We also introduce a new set of averaged equations that feature a global cosmological time despite the generality of the setting, and we put the statistical nature of effective cosmologies into perspective.

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“…In the case of perfect fluid sources, there are some inhomogeneous solutions that are, however, of no obvious cosmological relevance; see, e.g., Refs. [6,7,32]. Already this remark makes clear that a thoughtless application of the quasi-Newtonian metric form can quickly run into trouble: when the approximation made ignores the peculiar velocity terms in the field equations, it is in danger of running into effects related to these restrictions applying to the corresponding exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Geometrical order-of-magnitude estimates for spatial curvature in realistic models of the Universe

Buchert

Ellis

Elst³

2009

Gen Relativ Gravit

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11 pages. Fully hyperlinked. Dedicated to the memory of Jürgen Ehlers. To appear in the upcoming Special Issue of "General Relativity and Gravitation"International audienceThe thoughts expressed in this article are based on remarks made by Jürgen Ehlers at the Albert-Einstein-Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order-of-magnitude estimates for geometrical scalars, the relevance of spatial curvature in realistic models of the Universe that describe the dynamics of structure formation since the epoch of matter-radiation decoupling. We introduce these estimates with a commentary on the use of a quasi-Newtonian metric form in this context

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A class of shear-free perfect fluids in general relativity. II

Cited by 17 publications

References 28 publications

Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects

Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects

Cosmological backreaction and its dependence on spacetime foliation

Geometrical order-of-magnitude estimates for spatial curvature in realistic models of the Universe

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