![]() One model developed by American astronomers saw these clusters as high-density “meatballs” isolated in a low-density universe. Copernicus Astronomical Center (Warsaw) and one researcher from Cape Town University.īy the early 1980s, it was clear to astronomers that galaxies were not randomly distributed across the universe but instead, in many cases, concentrated in clusters. ![]() It is currently developed by a team composed of a researcher from the LUTH, two researchers from the N. An exact solution of general relativity able to model such “holes” exists, but it is much more difficult to implement because of its complexity. The models which appear the best adapted to solve this problem are Swiss-cheeses whose “holes” have no symmetry at all. But their “holes” were also spherically symmetric which made them rather unphysical and prevented them to solve efficiently the dark energy problem. New more realistic Swiss-cheese-type models have been used afterwards. But, of course, they could only consider radial inhomogeneities. Some among them were able to reproduce several cosmological data sets as well as or even better than the “concordance” model, without any need for dark energy. The first inhomogeneous models used to solve this problem were spherically symmetrical. The effect of the inhomogeneities was one of them. When the first observations of the light curves of remote type Ia supernovae were made, more than ten years ago, and when their interpretation in an homogeneous framework gave rise to the notion of dark energy, other proposals were made to explain these observations. However, the nature and properties of these new components are unknown in physics and they have been observed neither in laboratory experiments nor in the Universe. To make this so-called “concordance” model compatible with the cosmological data, more than 20% of dark matter and 75% of dark energy have been injected in it. Its main drawback is that 95% of the content of the Universe is unexplained. This is one of the reasons which contributed to the past and current success of the simplest model, the homogeneous model. The equations of general relativity are such involved that few exact analytical solutions usable in cosmology or astrophysics are known. Source: The problems of the homogeneous cosmological models Inhomogeneous models of universe : an alternative to dark energy Isotropic but not homogeneous? ⇒ Swiss Cheese Models.Homogeneous but not isotropic: Bianchi IX mixmaster models.Homogeneous and isotropic: Friedmann universe.Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology.Swiss-Cheese model based on an Einstein- de Sitter cosmology.Cosmology: dark matter – black hole physics.Spatially homogeneous and isotropic spacetime.320–399, Lecture Notes in Math., vol.Fractal and Multifractal Structures in Cosmology In: K-theory, Arithmetic and Geometry (Moscow, 1984–1986), pp. Wodzicki M.: Local invariants of spectral asymmetry. Princeton University Press, Princeton (2000) Voevodsly V., Suslin A., Friedlander E.M.: Cyles, Transfers, and Motivic Homology Theories. In: Geometric methods in the algebraic theory of quadratic forms, pp. Vishik, A.: Motives of quadrics with applications to the theory of quadratic forms. Max-Planck-Institut für Mathematik Bonn, Preprint MPI-1998-13, pp. Vishik, A.: Integral motives of quadrics. Suijlekom W.: Noncommutative Geometry and Particle Physics. (eds.) Mathematics Unlimited: 2001 and Beyond, pp. Gracia-Bondia J.M., Varilly J.C., Figueroa H.: Elements of Noncommutative Geometry. Goncharov, A.B., Spradlin, M., Vergu, C., Volovich, A.: Classical polylogarithms for amplitudes and Wilson loops. Golden J., Goncharov A.B., Spradlin M., Vergu C., Volovich A.: Motivic amplitudes and cluster coordinates. arXiv:1511.05321įathizadeh, F., Ghorbanpour, A., Khalkhali, M.: Rationality of spectral action for Robertson–Walker metrics. 10, 085 (2015)įan, W., Fathizadeh, F., Marcolli M.: Modular forms in the spectral action of Bianchi IX gravitational instantons. 76, 4073–4091 (2004)įan W., Fathizadeh F., Marcolli M.: Spectral action for Bianchi type-IX cosmological models. 34(3), 203–238 (1995)Ĭonnes, A., Marcolli, M.: Renormalization and motivic Galois theory. ![]() 10, 101 (2012)Ĭhamseddine A.H., Connes A.: The spectral action principle. ![]() Bloch S., Esnault H., Kreimer D.: On motives associated to graph polynomials.
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