General relativistic, nonstandard model for the dark sector of the Universe

Stichel, P.; Zakrzewski, W. J.

doi:10.1140/epjc/s10052-014-3218-3

Cited by 12 publications

(20 citation statements)

References 44 publications

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“…Then, according to (3) and (6), k 2 and k 3 must be positive [17], [18] leading by the constraint (14) to k 1 > 0. We conclude [19], [20]:…”

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

confidence: 65%

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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“…Then, according to (3) and (6), k 2 and k 3 must be positive [17], [18] leading by the constraint (14) to k 1 > 0. We conclude [19], [20]:…”

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

confidence: 65%

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

Stichel

2018

Phys. Rev. D

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“…We called it darkon fluid since it had been introduced initially for the description of the dark sector of the Universe. As argued in [9], the solution manifold contains also the baryonic matter as dust, though.…”

Section: Introductionmentioning

confidence: 94%

“…symmetry). Such an attempt has been made recently by the present author and by W. J. Zakrzewski [9]. Based on General Relativity (GR) we introduced a Lagrangian model containing no unknown parameters, which led to an energy-momentum tensor consisting of a dust term and a nontrivial energy flow [9].…”

Section: Introductionmentioning

confidence: 95%

Cosmological model with dynamical curvature

Stichel

2016

Preprint

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The recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) is generalized to a self-gravitating, irrotational, pressure-less and stress free geodesic fluid, whose energymomentum tensor is dust-like with nontrivial energy flow, defining the general framework for our cosmological model. In the present paper we consider only the averaged dynamics of the Universe at very large scales, allowing us to work with conformal flat geometry. The corresponding covariant propagation and constraint equations are treated in a shear-free nonrelativistic limit. The dynamics is described with a Lagrangian in minisuperspace. Analytic solutions for the energy density, the Hubble function and the 1st order relativistic correction to the spatial curvature are obtained by means of two conditional dynamical symmetries. This leads to a cosmological model where the accelerated expansion of the Universe is driven by a time-dependent spatial curvature without the need for introducing any kind of dark energy. A differential equation for the area distance is derived in addition.

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“…The subspace spanned by L 0 , L ±1 , J 0 , P i 0 , P i ±1 forms a ten dimensional subalgebra also called Galilean conformal algebra. It is known that this subalgebra has a peculiar central extension in the sense that it exists for only d = 2 and integral values of ℓ [2,6]. This exotic central extension makes the Abelian ideal P i m makes non-Abelian:…”

Section: Introductionmentioning

confidence: 99%

“…[P i m , P j n ] = I mn ǫ ij Θ, where I mn is a symmetric tensor. It is also known that the exotic Galilean conformal algebra has some physical applications [2,6]. (For more details on finite dimensional Galilean conformal algebras, see [7] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Some Properties of Planar Galilean Conformal Algebras

Aizawa

2013

Lie Theory and Its Applications in Physics

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Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2 + 1) dimensional spacetime and consider central extension. It is then shown that the Verma modules are irreducible for non-vanishing highest weights. This is done by explicit computation of Kac determinant. We also present coadjoint representations of the Galilean conformal algebra and its Lie group. As an application of them, a coadjoint orbit of the Galilean conformal group is given in a simple case.

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General relativistic, nonstandard model for the dark sector of the Universe

Cited by 12 publications

References 44 publications

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

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

Cosmological model with dynamical curvature

Some Properties of Planar Galilean Conformal Algebras

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