A gradient expansion for cosmological backreaction

Journal of Cosmology and Astroparticle Physics (Impact Factor: 5.81). 12/2011; 2012(03). DOI: 10.1088/1475-7516/2012/03/026
Source: arXiv


We address the issue of cosmological backreaction from non-linear structure
formation by constructing an approximation for the time evolved metric of a
dust dominated universe based on a gradient expansion. Our metric begins as a
perturbation of a flat Friedmann-Robertson-Walker state described by a nearly
scale invariant, Gaussian, power-law distribution, and evolves in time until
non-linear structures have formed. After describing and attempting to control
for certain complications in the implementation of this approach, this metric
then forms a working model of the universe. We numerically calculate the
evolution of the average scale factor in this model and hence the backreaction.
We argue that, despite its limitations, this model is more realistic than
previous models that have confronted the issue of backreaction. We find that
the \emph{instantaneous} effects of backreaction in this model could be as
large as $\sim10%$ of the background. This suggests that a proper understanding
of the \emph{cumulative} effects of backreaction could be crucial for precision
cosmology and any future exploration of the dark sector.

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    • "It as also proved useful in studying the backreaction of cosmic structure formation, see [18] and arXiv:1203.2796v2 [astro-ph.CO] 18 Oct 2012 more recently [19]. In most of past works the gradient expansion has been applied directly on the Einstein equations. "
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    ABSTRACT: We describe inhomogeneities in a {\Lambda}CDM universe with a gradient series expansion and show that it describes the gravitational evolution far into the non-linear regime and beyond the capacity of standard perturbation theory at any order. We compare the gradient expansion with exact inhomogeneous {\Lambda}LTB solutions (Lema\^itre-Tolman-Bondi metric with the inclusion of a cosmological constant) describing growing structure in a {\Lambda}CDM universe and find that the expansion approximates the exact solution well, following the collapse of an over-density all the way into a singularity.
    Physical review D: Particles and fields 08/2012; 86(4). DOI:10.1103/PhysRevD.86.043523 · 4.86 Impact Factor
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    • "Developed in [25] [53] and used in [35] to study backreaction, this technique—contrary to perturbation theory—seems to take better care of the impact of the small-scale nonlinear effects on the larger ones. A recent study [29] has shown that, already for gradient expansion quantities of the 4 th -level, the effects of backreaction grows to 5–10% of the background. A realization of this iterative strategy is the subject of forthcoming work. "
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    ABSTRACT: In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.
    Classical and Quantum Gravity 02/2012; 29(11). DOI:10.1088/0264-9381/29/11/115004 · 3.17 Impact Factor
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    ABSTRACT: Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore important to understand which degrees of freedom and which features are lost when the relativistic universe is approximated, or rather replaced, by a Newtonian one. This is the main purpose of our investigation. We first define Newtonian cosmology and we give an overview on general relativity, both in its standard and covariant formulations. We show how the two theories deal with inhomogeneous cosmological models and we introduce the backreaction conjecture. Then we review on how Newtonian gravity and general relativity relate to each other in the fully non-linear regime. For this purpose we discuss frame theory. We carry out the same investigation also in the weak-field, small-velocity limit of general relativity, and we derive the Newtonian limit resorting to the framework of post-Newtonian cosmology. Finally we remark that there are solutions of Newtonian gravity which do not have any relativistic counterpart.
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