Light propagation and the average expansion rate in near-FRW universes

A persistent theme in the study of dark energy is the question of whether it really exists or not. It is often claimed that we are mis-calculating the cosmological model by neglecting the effects associated with averaging over large-scale structures. In the Newtonian approximation this is clear: there is no effect. Within the full relativistic picture this remains an important open question, owing to the complex mathematics involved. We study this issue using numerical N-body simulations which account for all relevant relativistic effects without any problems from shell crossing. In this context we show for the first time that the backreaction from structure can differ by many orders of magnitude depending upon the slicing of spacetime one chooses to average over. In the worst case, where smoothing is carried out in synchronous spatial surfaces, the corrections can reach ten percent and more. However, when smoothing on the constant time hypersurface of the Newtonian gauge, backreaction contributions remain 3-5 orders of magnitude smaller.PACS numbers: 95.36.+x, 98.80.Es

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“…This was expected from theoretical considerations, see e.g. [53,54], but we quantify this statement numerically.…”

Section: Discussionmentioning

confidence: 75%

Safely smoothing spacetime: backreaction in relativistic cosmological simulations

Adamek

Clarkson

Daverio

et al. 2018

Class. Quantum Grav.

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“…It is supposed to represent the 4−velocity field of the observers. In the application paper [75], this field is restricted to be everywhere very close to n (and so has a small vorticity), whereas n is assumed to be chosen such that it builds hypersurfaces of statistical homogeneity and isotropy. These restrictions are already both suggested in the original paper [74] but the equations are kept general.…”

Section: Smirnov [82]mentioning

confidence: 99%

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

2020

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We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in floworthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated 1 + 3 threading congruence, used jointly with the 3 + 1 foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.

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“…We emphasize that this interpretation tacitly considers the averaged expansion rate as the relevant physical quantity to describe the dynamics of the Universe, which is a highly non-trivial, and widely debated assumption. Notable contributions to this debate [55,[73][74][75] concluded that, in a fluid-filled and shell-crossing-free universe, the spatially averaged expansion rate really governs the angular distance-redshift relation, and therefore has a powerful physical and observational meaning. However, there is a priori not reason why this result should hold for a more realistic description of the Universe, with shell crossings, formation of virialised structures decoupled from the expansion, etc.…”

Section: Backreaction and Swiss-cheese Modelsmentioning

confidence: 99%

Swiss-cheese models and the Dyer-Roeder approximation

Fleury

2014

J. Cosmol. Astropart. Phys.

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Abstract. In view of interpreting the cosmological observations precisely, especially when they involve narrow light beams, it is crucial to understand how light propagates in our statistically homogeneous, clumpy, Universe. Among the various approaches to tackle this issue, Swisscheese models propose an inhomogeneous spacetime geometry which is an exact solution of Einstein's equation, while the Dyer-Roeder approximation deals with inhomogeneity in an effective way. In this article, we demonstrate that the distance-redshift relation of a certain class of Swiss-cheese models is the same as the one predicted by the Dyer-Roeder approach, at a well-controlled level of approximation. Both methods are therefore equivalent when applied to the interpretation of, e.g., supernova obervations. The proof relies on completely analytical arguments, and is illustrated by numerical results.

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Light propagation and the average expansion rate in near-FRW universes

Cited by 32 publications

References 125 publications

Safely smoothing spacetime: backreaction in relativistic cosmological simulations

Safely smoothing spacetime: backreaction in relativistic cosmological simulations

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

Swiss-cheese models and the Dyer-Roeder approximation

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