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58
Cosmological NonLinearities as an Effective Fluid
 JCAP
"... The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that smallscale nonlinearities do not induce a large backreaction? Related to this, what is the effective theo ..."
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Cited by 23 (5 self)
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The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that smallscale nonlinearities do not induce a large backreaction? Related to this, what is the effective theory that describes the universe on large scales? In this paper we make progress in addressing these questions. We show that the effective theory for the longwavelength universe behaves as a viscous fluid coupled to gravity: integrating out shortwavelength perturbations renormalizes the homogeneous background and introduces dissipative dynamics into the evolution of longwavelength perturbations. The effective fluid has small perturbations and is characterized by a few parameters like an equation of state, a sound speed and a viscosity parameter. These parameters can be matched to numerical simulations or fitted from observations. We find that the backreaction of smallscale nonlinearities is very small, being suppressed by the large hierarchy between the scale of nonlinearities and the horizon scale. The effective pressure of the fluid is always positive and much too small to significantly affect the background evolution. Moreover, we prove that virialized scales decouple completely from the largescale dynamics, at all orders in the postNewtonian expansion. We propose that our effective theory be used to formulate a welldefined and controlled alternative to conventional perturbation theory, and we discuss possible observational applications. Finally, our way of reformulating results in secondorder perturbation theory in terms of a longwavelength effective fluid provides the opportunity to understand nonlinear effects in a simple and physically intuitive way. ar X iv
Modified Newtonian dynamics (MOND): Observational phenomenology and relativistic extensions
 Living Reviews in Relativity
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Light propagation in statistically homogeneous and isotropic dust universes
, 2009
"... We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the DyerRoeder approximation does not correctly describe the effect of ..."
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Cited by 21 (2 self)
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We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the DyerRoeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat ΛCDM model.
Swiss Cheese and a Cheesy CMB
, 902
"... Abstract: It has been argued that the SwissCheese cosmology can mimic Dark Energy, when it comes to the observed luminosity distanceredshift relation. Besides the fact that this effect tends to disappear on average over random directions, we show in this work that based on the ReesSciama effect o ..."
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Cited by 9 (3 self)
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Abstract: It has been argued that the SwissCheese cosmology can mimic Dark Energy, when it comes to the observed luminosity distanceredshift relation. Besides the fact that this effect tends to disappear on average over random directions, we show in this work that based on the ReesSciama effect on the cosmic microwave background (CMB), the SwissCheese model can be ruled out if all holes have a radius larger than about 35 Mpc. We also show that for smaller holes, the CMB is not observably affected, and that the small holes can still mimic Dark Energy, albeit in special directions, as opposed to previous conclusions in the literature. However, in this limit, the probability of looking in a special direction where the luminosity of supernovae is sufficiently supressed becomes very small, at least in the case of a lattice of spherical holes considered in this paper. Laboratoire d’AnnecyleVieux de Physique Théorique, UMR5108Contents
On the curvature of the present day Universe
, 2008
"... Abstract. We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present–day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to assume that curvature averages out on some scale ..."
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Cited by 9 (5 self)
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Abstract. We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present–day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to assume that curvature averages out on some scale of homogeneity, as implied by the standard concordance model of cosmology, or whether the averaged scalar curvature can be largely negative today, as required for an explanation of Dark Energy from inhomogeneities. We confront both conjectures with a detailed analysis of the kinematical backreaction term and estimate its strength for a multi– scale inhomogeneous matter and curvature distribution. Our main result is a formula for the spatially averaged scalar curvature involving quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We propose strategies to quantitatively evaluate the formula, and pinpoint the assumptions implied by the conjecture of a small or zero averaged curvature. We reach the conclusion that the standard concordance model needs fine–tuning in the sense of an assumed equipartition law for curvature in order to reconcile it with the estimated properties of the averaged physical space, whereas a negative averaged curvature is favoured, independent of the prior on the value of the cosmological constant.
Elst: Geometrical order–of–magnitude estimates for spatial curvature in realistic models of the Universe
"... The 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 c ..."
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Cited by 8 (5 self)
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The 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. PACS number(s): 04.20.q, 04.20.Cv, 98.80.k, 98.80.Jk Preprint number(s): arXiv:0906.0134 [grqc]
Exploiting scale dependence in cosmological averaging [0708.3673
"... Abstract: We study the role of scale dependence in the Buchert averaging method, using the flat LemaitreTolmanBondi model as a testing ground. Within this model, a single averaging scale gives too coarse predictions, but by replacing it with the distance of the objects R(z) for each redshift z, we ..."
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Cited by 7 (0 self)
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Abstract: We study the role of scale dependence in the Buchert averaging method, using the flat LemaitreTolmanBondi model as a testing ground. Within this model, a single averaging scale gives too coarse predictions, but by replacing it with the distance of the objects R(z) for each redshift z, we find an O(1%) precision at z < 2 in the averaged luminosity and angular diameter distances compared to their exact expressions. At low redshifts, we show the improvement for generic inhomogeneity profiles, and our numerical computations further verify it up to redshifts z ∼ 2. At higher redshifts, the method breaks down due to its inability to capture the time evolution of the inhomogeneities. We also demonstrate that the running smoothing scale R(z) can mimic acceleration, suggesting it could be at least as important as the backreaction in explaining dark energy as an inhomogeneity induced illusion.