Cosmological backreaction from perturbations

Behrend, Juliane; Brown, Iain A.; Robbers, Georg

doi:10.1088/1475-7516/2008/01/013

Cited by 55 publications

(82 citation statements)

References 92 publications

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“…At second order, as at first order, we split the generating vector ξ µ 2 into a scalar time and scalar and vector spatial part, similarly as at first order, as 19) where the vector part is divergence-free ∂ k γ k 2 = 0. We then find from Eqs.…”

Section: Second Ordermentioning

confidence: 99%

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Cosmological perturbations

Malik¹,

Wands²

2009

Physics Reports

551

862

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We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.

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Section: Second Ordermentioning

confidence: 99%

“…Recently it has also become popular in backreaction studies, e.g. [19,71,170]. After imposing the gaugeconditions the metric tensor is diagonal, which simplifies many calculations, for example the derivation of the governing equations of the Boltzmann-hierarchy.…”

Section: First Ordermentioning

confidence: 99%

Cosmological perturbations

Malik¹,

Wands²

2009

Physics Reports

551

862

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“…This deviation has recently been quantified in the framework of perturbation theory [35,36,37] (see also [38] for an estimation in the conformal Newtonian gauge), and since we have arguments why a non-perturbative treatment is necessary for the effects of interest, we shall consider the dominant perturbative mode within a general class of scaling solutions to a backreaction-driven cosmology. Of course, the scaling solutions cannot be expected to fully represent the realistic backreaction effect throughout the whole history of the Universe, but it is considered here for reasons of clarity and simplicity to illustrate the kind of effects expected from the non-trivial geometry, in analogy to studies using parameterizations of the equation of state for Dark Energy.…”

Section: Introductionmentioning

confidence: 99%

Testing backreaction effects with observations

et al. 2009

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Abstract. In order to quantitatively test the ability of averaged inhomogeneous cosmologies to correctly describe observations of the large scale properties of the Universe, we introduce a smoothed template metric corresponding to a constant spatial curvature model at any time, but with an evolving curvature parameter. This metric is used to compute quantities along an approximate effective lightcone of the averaged model of the Universe. As opposed to the standard Friedmann model, we parameterize this template metric by exact scaling properties of an averaged inhomogeneous cosmology, and we also motivate this form of the metric by results on a geometrical smoothing of inhomogeneous cosmological hypersurfaces. The purpose of the paper is not to demonstrate that the backreaction effect is actually responsible for the Dark Energy phenomenon by explicitly calculating the effect from a local model of the geometry and the distribution of matter, but rather to propose a way to deal with observations in the backreaction context, and to understand what kind of generic properties have to hold in order for a backreaction model to explain the observed features of the Universe on large scales. We test our hypothesis for the template metric against supernova data and the position of the CMB peaks, and infer the goodness-of-fit and parameter uncertainties. We find that averaged inhomogeneous models can reproduce the observations without requiring an additional Dark Energy component (though a volume acceleration is still needed), and that current data do not disfavour our main assumption on the effective lightcone structure. We also show that the experimental uncertainties on the angular diameter distance and the Hubble parameter from Baryon Acoustic Oscillations measurements -forseen in future surveys like the proposed EUCLID satellite project -are sufficiently small to distinguish between a FLRW template geometry and the template geometry with consistently evolving curvature.

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“…A critical problem in cosmology is therefore determining the form of deviations from Einstein's equations when considering geometry averaged on large scales, and what the effects of these deviations will be on observations (for a review, see [1]). This has been the subject of some controversy, with opinions ranging from the suggestion that the effects of averaging could completely explain the recently observed accelerating expansion of the Universe without the need for any dark energy [2][3][4][5][6][7][8][9], to the claim that it is completely negligible [10][11][12][13][14][15][16][17][18][19][20][21]. Others suggest that while the effects of averaging may not be responsible for the apparent acceleration, they may be important for precision cosmology [22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Observational constraints on the averaged universe

et al. 2012

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Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not yield the same result as solving Einstein's equations with a smooth matter distribution, and that the smooth models we fit to observations need not be simply related to the actual geometry of spacetime. One specific consequence of this is a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvature in the Friedmann equation. Here we investigate the consequences of this decoupling by fitting to a combination of HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial curvature is tightly constrained, and that our ability to constrain dark energy dynamics will be severely impaired until we gain a thorough understanding of the averaging problem in cosmology.

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Cosmological backreaction from perturbations

Cited by 55 publications

References 92 publications

Cosmological perturbations

Cosmological perturbations

Testing backreaction effects with observations

Observational constraints on the averaged universe

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