Cosmological model with dynamical curvature

Stichel, Peter C.

doi:10.48550/arxiv.1601.07030

Cited by 7 publications

(12 citation statements)

References 29 publications

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“…[See also recent work on averaging of LTB (Sussman et al 2015;Chirinos Isidro et al 2016) and Szekeres models (Bolejko 2009); for evolving sign-of-curvature models, see e.g. Krasinski (1981Krasinski ( , 1982Krasinski ( , 1983; Stichel (2016); for averaging using Cartan scalars, see Coley (2010); Kašpar & Svítek (2014) (Lemaître 1927; see also Hubble 1929), is another key property that should emerge in a relativistic cosmological model. If this ratio is as small as Roukema et al 2013), then, through Eqs.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…In the nonrelativistic and shear-free limit [19] (or at small distances [20]) we obtain from the EEs, after having eliminated the energy flow vector, the following system of two coupled ordinary differential equations for the cosmological scale factor a(t) and the active gravitational mass density (for any details we refer to [19] and [20] respectively).…”

Section: Summary Of the Nonrelativistic Cosmological Model (Nrcm)mentioning

confidence: 99%

“…Recently we have shown that a nonrelativistic cosmological model (NRCM) introduced in [17], reviewed in [18] and derived as the nonrelativistic limit (approximation at sub-Hubble scales) of a general relativistic model exhibits a dynamical curvature function with a negative value at the present cosmological epoch [19], [20]. In a very recent paper [1] we have fixed the three constants (initial conditions) of the model by adjusting them in two different ways to a second order polynomial fit by Montanari and Räsänen [21] to the observed expansion rate H(z).…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for two inhomogeneous cosmological models with energy flow and dynamical curvature

Stichel

2018

Phys. Rev. D

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Recently we have introduced a nonrelativistic cosmological model (NRCM) exhibiting a dynamical spatial curvature. For this model the present day cosmic acceleration is not attributed to a negative pressure (dark energy) but it is driven by a nontrivial energy flow leading to a negative spatial curvature. In this paper we generalize the NRCM in two different ways to the relativistic regime and present analytical solutions of the corresponding Einstein equations. These relativistic models are characterized by two inequivalent extensions of the FLWR metric with a time-dependent curvature function K(t) and an expansion scalar a(t). The fluid flow is supposed to be geodesic. The model V1 is shear-free with isotropic pressure and therefore conformal flat. It shows some common properties with the spherically symmetric Stephani models but it exhibits also some specific differences. In contrast to V1 the second model V2 shows a nontrivial shear and an anisotropic pressure. For both models the inhomogeneous solutions of the corresponding Einstein equations will agree in leading order at small distances with the NRCM if a(t) and K(t) are each identical with those determined in the NCRM. This will be achieved by the demand of vanishing isotropic pressure and its first derivative w.r.t. r 2 at the coordinate origin r = 0. Then the metric is completely fixed by three constants. The arising energy momentum tensor contains a nontrivial energy flow vector. Our models violate locally the weak energy condition. As this may be caused by some averaging we speculate about to view each of our models as a local average of some other more fundamental model. Global volume averaging leads to explicit expressions for the effective scale factor and the expansion rate H(z). Backreaction effects cancel each other for the model V2 but they are nonzero and proportional to the square of the magnitude of the energy flow for the model V1. The large scale (relativistic) corrections to the NCRM results are small for the model V2 for a small-sized energy flow. We have reproduced a corresponding adjustment of the three free constants from [1] to cosmic chronometer data leading to the prediction of an almost constant, negative value for the dimensionless curvature function k(z) ∼ −1 for redshifts z < 2.

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“…Accurate modelling of non-linear 3-Ricci (spatial) curvature is a key challenge that all of these software packages need to meet if they are to be used to test the hypothesis that structure formation leads to recently emerging negative mean curvature that physically explains 'dark energy' (Räsänen 2006;Nambu & Tanimoto 2005;Kai et al 2007;Räsänen 2008;Larena et al 2009;Chiesa et al 2014;Wiegand & Buchert 2010;Buchert & Räsänen 2012;Wiltshire 2009;Duley et al 2013;Nazer & Wiltshire 2015;Roukema et al 2013;Barbosa et al 2016;Bolejko & Célérier 2010;Lavinto et al 2013;Roukema 2018;Sussman et al 2015;Chirinos Isidro et al 2017;Bolejko 2017b,a;Krasinski 1981Krasinski , 1982Krasinski , 1983Stichel 2016Stichel , 2018Coley 2010;Kašpar & Svítek 2014;Rácz et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Does relativistic cosmology software handle emergent volume evolution?

Borkowska,

Roukema

2021

Preprint

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Several software packages for relativistic cosmological simulations that do not fully implement the Einstein equation have recently been developed. Two of the free-licensed ones are and . A key question is whether globally emergent volume evolution that is faster than that of a Friedmannian reference model results from the averaged effects of structure formation. Checking that emergent volume evolution is correctly modelled by the packages is thus needed. We numerically replace the software's default random realisation of initial seed fluctuations by a fluctuation of spatially constant amplitude in a simulation's initial conditions. The average volume evolution of the perturbed model should follow that of a Friedmannian expansion history that corresponds to the original Friedmannian reference solution modified by the insertion of the spatially constant perturbation. We find that allows emergent volume evolution correctly at first order through to the current epoch. For initial conditions with a resolution of = 128 3 particles and an initial non-zero extrinsic curvature invariant I i = 0.001, matches an exact Friedmannian solution to −0.00576% (Einstein-de Sitter, EdS) or −0.00326% (ΛCDM). We find that models the decaying mode to fair accuracy, and excludes the growing mode by construction. For = 128 3 and an initial scalar potential Φ = 0.001, is accurate for the decaying mode to 0.0125% (EdS) or 0.0125% (ΛCDM). We conclude that this special case of an exact non-linear solution for a perturbed Friedmannian model provides a robust calibration for relativistic cosmological simulations.

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Cosmological model with dynamical curvature

Cited by 7 publications

References 29 publications

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

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

Analytical solutions for two inhomogeneous cosmological models with energy flow and dynamical curvature

Does relativistic cosmology software handle emergent volume evolution?

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