Lagrangian theory of structure formation in relativistic cosmology. III. Gravitoelectric perturbation and solution schemes at any order

Alles, Alexandre; Buchert, Thomas; Roumi, Fosca Al; Wiegand, Alexander

doi:10.1103/physrevd.92.023512

Cited by 28 publications

(37 citation statements)

References 40 publications

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“…To reconstruct the primordial comoving galaxy positions more accurately than in the standard model, i.e. to allow flexible comoving curvature that varies with the matter density and the extrinsic curvature tensor across a spatial slice, relativistic Lagrangian perturbation theory (Buchert & Ostermann 2012;Buchert, Nayet & Wiegand 2013;Alles et al 2015) is available for analytically guided calculations. N-body simulations in which the growth of inhomogeneities is matched by inhomogeneous metric evolution will most likely also be needed to develop numerical confidence in what could be called "relativistic BAO reconstruction".…”

Section: Discussionmentioning

confidence: 99%

Is the baryon acoustic oscillation peak a cosmological standard ruler?

Roukema

Buchert

Fujii

et al. 2015

Monthly Notices of the Royal Astronomical Society: Letters

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In the standard model of cosmology, the Universe is static in comoving coordinates; expansion occurs homogeneously and is represented by a global scale factor. The baryon acoustic oscillation (BAO) peak location is a statistical tracer that represents, in the standard model, a fixed comoving-length standard ruler. Recent gravitational collapse should modify the metric, rendering the effective scale factor, and thus the BAO standard ruler, spatially inhomogeneous. Using the Sloan Digital Sky Survey, we show to high significance (P < 0.001) that the spatial compression of the BAO peak location increases as the spatial paths' overlap with superclusters increases. Detailed observational and theoretical calibration of this BAO peak location environment dependence will be needed when interpreting the next decade's cosmological surveys.

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Section: Discussionmentioning

confidence: 99%

Is the baryon acoustic oscillation peak a cosmological standard ruler?

Roukema

Buchert

Fujii

et al. 2015

Monthly Notices of the Royal Astronomical Society: Letters

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“…Such a transformation does not require a 'Newtonian limit' (referring to a limit where the inverse of a causality constant goes to zero, 1/c → 0; for a detailed discussion of this notion, see [29]). It rather requires a restriction of the fluid deformations to integrable fluid deformations, named Minkowski Restriction (henceforth MR), defined and executed for various variables in a fluid-orthogonal framework in the series of papers [33,31,2,3,66], see especially [2,3]. The cosmological equations presented in this paper do not assume any particular spatial metric or any specific explicit form for the twice-covariant fluidorthogonal projecting tensor b = b µν dx µ ⊗ dx ν : they only depend functionally on these tensors.…”

Section: Recovering the Newtonian Form Of The Effective Cosmological 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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“…However, by evolving an initial power spectrum of density perturbations from an early epoch forward in foliation time, predictions of t 0 that differ from the ΛCDM value can also be made. For example, this evolution can be calculated using the relativistic Zel'dovich approximation (Kasai 1995;Morita et al 1998) in the form given by Buchert & Ostermann (2012); Buchert et al (2013); Alles et al (2015); see also Matarrese & Terranova (1996); Villa et al (2011).…”

Section: Astrophysical Age Of Universe Estimates As a Test Of Inhomogmentioning

confidence: 99%

The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe

Roukema

Mourier

Buchert

et al. 2017

A&A

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Context. In relativistic inhomogeneous cosmology, structure formation couples to average cosmological expansion. A conservative approach to modelling this assumes an Einstein-de Sitter model (EdS) at early times and extrapolates this forward in cosmological time as a "background model" against which average properties of today's Universe can be measured. Aims. This requires adopting an early-epoch-normalised background Hubble constant H bg 1 .Methods. Here, we show that the ΛCDM model can be used as an observational proxy to estimate H bg 1 rather than choose it arbitrarily. We assume (i) an EdS model at early times; (ii) a zero dark energy parameter; (iii) bi-domain scalar averaging-division of the spatial sections into over-and underdense regions; and (iv) virialisation (stable clustering) of collapsed regions. Results. We find H bg 1 = 37.7 ± 0.4 km/s/Mpc (random error only) based on a Planck ΛCDM observational proxy. Conclusions. Moreover, since the scalar-averaged expansion rate is expected to exceed the (extrapolated) background expansion rate, the expected age of the Universe should be much less than 2/(3H bg 1 ) = 17.3 Gyr. The maximum stellar age of Galactic Bulge microlensed low-mass stars (most likely: 14.7 Gyr; 68% confidence: 14.0-15.0 Gyr) suggests an age about a Gyr older than the (no-backreaction) ΛCDM estimate.

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Lagrangian theory of structure formation in relativistic cosmology. III. Gravitoelectric perturbation and solution schemes at any order

Cited by 28 publications

References 40 publications

Is the baryon acoustic oscillation peak a cosmological standard ruler?

Is the baryon acoustic oscillation peak a cosmological standard ruler?

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

The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe

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