On the role of shear in cosmological averaging

Mattsson, Maria; Mattsson, Teppo

doi:10.1088/1475-7516/2010/10/021

Cited by 24 publications

(34 citation statements)

References 53 publications

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“…As such, the Buchert average deceleration parameter q D , defined in Eq. (21), is dominated by the same terms that appear in the definitions of the Kristian-Sachs and local volume measures, most notably the density. Our different measures of acceleration do not exactly reduce to one another in this case, but they are rather close (as can be seen in Figure 10, inset).…”

Section: Results: Ltbmentioning

confidence: 99%

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: Results: Ltbmentioning

confidence: 99%

Local and nonlocal measures of acceleration in cosmology

Bull

Clifton

2012

Phys. Rev. D

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“…where dV p is the proper volume element (11), F is the weight factor (12) and V p0 is the proper volume of any given domain D[r] evaluated at an arbitrary t = t 0 . Comparing (50) and (51) leads to the relation:…”

Section: Scale Factors and Reference Volumesmentioning

confidence: 99%

Weighed scalar averaging in LTB dust models: part I. Statistical fluctuations and gravitational entropy

Sussman¹

2013

Class. Quantum Grav.

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We introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaître-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuation. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302-14). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfillment in various LTB models and regions. While the q-average formalism is specially suited for LTB (and Szekeres) models, it may provide a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes in general.PACS numbers: 98.80.-k, 04.20.-q, 95.36.+x, 95.35.+d arXiv:1209

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“…In this form, it is implicit that the influence of the Weyl tensor (shear) can be neglected. This means that the light rays are propagating far from the mass inhomogeneities so that the large-scale homogeneity implies that their shear contribution are canceled [35]. Further, the Ricci tensor R µν is related to the energy momentum tensor T µν through the Einstein field equations:…”

Section: Zkdr Equation For Luminosity Distancementioning

confidence: 99%

Constraining the dark energy and smoothness parameter with type Ia supernovae and gamma-ray bursts

Busti¹,

Santos²,

Lima³

2012

Phys. Rev. D

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The existence of inhomogeneities in the observed Universe modifies the distance-redshift relations thereby affecting the results of cosmological tests in comparison to the ones derived assuming spatially uniform models. By modeling the inhomogeneities through a Zeldovich-Kantowski-DyerRoeder (ZKDR) approach which is phenomenologically characterized by a smoothness parameter α, we rediscuss the constraints on the cosmic parameters based on type Ia Supernovae (SNe Ia) and Gamma-Ray Bursts (GRBs) data. The present analysis is restricted to a flat ΛCDM model with the reasonable assumption that Λ does not clump. A χ 2 -analysis using 557 SNe Ia data from and α ≥ 0.52. As a general result, although considering that current GRB data alone cannot constrain the smoothness α parameter our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities.PACS numbers: 95.35.+d, 95.36.+x,98.70.Rz,97.60.Bw

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On the role of shear in cosmological averaging

Cited by 24 publications

References 53 publications

Local and nonlocal measures of acceleration in cosmology

Local and nonlocal measures of acceleration in cosmology

Weighed scalar averaging in LTB dust models: part I. Statistical fluctuations and gravitational entropy

Constraining the dark energy and smoothness parameter with type Ia supernovae and gamma-ray bursts

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