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Friedmann–Lemaître–Robertson–Walker metric

About: Friedmann–Lemaître–Robertson–Walker metric is a research topic. Over the lifetime, 4113 publications have been published within this topic receiving 87752 citations. The topic is also known as: FLRW metric.


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Journal ArticleDOI
TL;DR: In this paper, an approximate, general-relativistic correction to the matter-dominated (Omega_m = 1, Omega_Lambda=0), homogeneous metric (Einstein de Sitter, EdS) was proposed.
Abstract: The geometry of the dark energy and cold dark matter dominated cosmological model (LambdaCDM) is commonly assumed to be given by a Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, i.e. it assumes homogeneity in the comoving spatial section. The homogeneity assumption fails most strongly at (i) small distance scales and (ii) recent epochs, implying that the FLRW approximation is most likely to fail at these scales. We use the virialisation fraction to quantify (i) and (ii), which approximately coincide with each other on the observational past light cone. For increasing time, the virialisation fraction increases above 10% at about the same redshift (sim 1-3) at which Omega_Lambda grows above 10% (approx 1.8). Thus, instead of non-zero Omega_Lambda, we propose an approximate, general-relativistic correction to the matter-dominated (Omega_m =1, Omega_Lambda=0), homogeneous metric (Einstein de Sitter, EdS). A low-redshift effective matter-density parameter of Omega_m^eff(0) = 0.26 pm 0.05 is inferred. Over redshifts 0 < z < 3, the distance modulus of the virialisation-corrected EdS model approximately matches the LambdaCDM distance modulus. This rough approximation assumes "old physics" (general relativity), not "new physics". Thus, pending more detailed calculations, we strengthen the claim that "dark energy" should be considered as an artefact of emerging average curvature in the void-dominated Universe, via a novel approach that quantifies the relation between virialisation and average curvature evolution.

41 citations

01 Nov 1996
TL;DR: In this paper, an extension of the 1+3 decomposition formalism is presented, partially in fully covariant form, and partially on the basis of choice of an arbitrary Minkowskian orthonormal reference frame, the timelike direction of which is aligned with u=c.
Abstract: 1 + 3 “threading” decomposition methods of the pseudo-Riemannian spacetime manifold (M;g) and all itsgeometrical objects and dynamical relations with respect to an invariantly defined preferred timelike referencecongruence u=chave been useful tools in general relativistic cosmological modelling for more than three decades.In this thesis extensions of the 1+3 decomposition formalism are developed, partially in fully covariant form, andpartially on the basis of choice of an arbitrary Minkowskian orthonormal reference frame, the timelike directionof which is aligned with u=c. After introductory remarks, in Chapter 2 first an exposition is given of the general1 + 3 covariant dynamical equations for the fluid matter and Weyl curvature variables, which arise from the Ricciand second Bianchi identities for the Riemann curvature tensor of (M;g;u=c). New evolution equations arethen derived for all spatial derivative terms of geometrical quantities orthogonal to u=c. The latter are used todemonstrate in 1 + 3 covariant terms that the spatial constraints restricting relativistic barotropic perfect fluidspacetime geometries are preserved along the integral curves of u=c. The integrability of a number of differentspecial subcases of interest can easily be derived from this general result.In Chapter 3, 1 + 3 covariant representations of two classes of well-known cosmological models with abarotropic perfect fluid matter source are obtained. These are the families of the locally rotationally symmetric(LRS) and the orthogonally spatially homogeneous (OSH) spacetime geometries, respectively. Subcases arisingfrom either dynamical restrictions or the existence of higher symmetries are systematically discussed. For exam-ple, models of purely “magnetic” Weyl curvature and, in the LRS case, a transparent treatment of tilted spatialhomogeneity can be obtained. The 1 + 3 covariant discussion of the OSH models requires completion.Chapter 4 reviews the complementary 1 + 3 orthonormal frame (ONF) approach and extends it to includethe second Bianchi identities, which provide dynamical relations for the physically interesting Weyl curvaturevariables. Then, possible choices of local coordinates within the 1+3 ONF framework are introduced, taking boththe 1 + 3 threading and the ADM 3 + 1 slicing perspectives.The 1 + 3 ONF method is employed in Chapter 5 to investigate the integrability of the dynamical equationsdescribing “silent” irrotational dust spacetime geometries, for which the “magnetic” part of the Weyl curvature isrequired to vanish. Evidence is obtained that these equations may not be consistent in the generic case, but thatonly either algebraically special or spatially homogeneous classes of solutions may be covered. Furthermore, thischapter uses the extended 1 + 3 ONF dynamical equations to describe LRS models with an imperfect fluid mattersource and contrasts the perfect fluid subcase with the results obtained in Chapter 3.In Chapter 6, a brief detour is taken into considering those classical theories of gravitation in which the La-grangean density of the gravitational field is assumed to be proportional to a general differentiable function f(R)in the Ricci curvature scalar. The generalisations of the relativistic 1 + 3 covariant dynamical equations to thef(R) case are derived and a few examples of applications are commented on.Finally, Chapter 7 investigates in detail features of the dynamical evolution of the cosmological density pa-rameter in anisotropic inflationary models of Bianchi Type–I and Type–V and points out important qualitativechanges as compared to the idealised standard FLRW situation. A related analysis employing the same spacetimegeometries addresses the occurrence of restrictions on the permissible functional form of the inflationary expansionlength scale parameter Sas a consequence of the so-called reality condition for Einstein–Scalar-Field configura-tions. Again, the effect of the (exact) anisotropic perturbations on the FLRW case is thoroughly studied and foundto have significant effects. Both cases can be treated as examples of structural instability.This thesis ends with concluding remarks and an appendix section containing the conventions employed andmathematical relations relevant to derivations given in various chapters.

41 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate locally rotational symmetric Bianchi type I spacetimes with non-minimally coupled scalar fields and find exact solutions of the equations of motion in terms of three parameters and an arbitrary function.
Abstract: Following up on hints of anisotropy in the cosmic microwave background radiation (CMB) data, we investigate locally rotational symmetric (LRS) Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke (BD) field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and an arbitrary function. We illustrate with families of examples designed to be generalizations of the well-known power-expansion, exponential expansion and Big Rip models in the Friedmann-Robertson-Walker (FRW) framework. The solutions display surprising variation, a large subset of which features late-time acceleration as is usually ascribed to dark energy (phantom or quintensence), and is consistent with observational data.

41 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the correspondence between the interacting new agegraphic dark energy and the polytropic gas model of dark energy in the non-flat FRW universe.
Abstract: We study the correspondence between the interacting new agegraphic dark energy and the polytropic gas model of dark energy in the non-flat FRW universe. This correspondence allows us to reconstruct the potential and the dynamics for the scalar field of the polytropic model, which describe accelerated expansion of the universe.

41 citations

Journal ArticleDOI
TL;DR: In this paper, a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epochs is presented.

41 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023150
2022352
2021196
2020204
2019214
2018191